The subject of Airbeds in general brings up the differences between active support and passive support.
Foam and springs (and even horse hair) offer more active support. In other words they not only resist compression and stop you from sinking into a mattress past a certain point but they are also more resilient and adaptive because they "push back" against compression. Air, water, memory foam, various types of natural fibers (wool, cotton, stuffed rags, etc), and buckling column gel offer more passive support that is less resilient and can affect the ease of movement on the mattress and may not adapt as well to different sleeping positions. It is the same kind of support that would be offered by a piece of wood that was carved to your exact body profile. If this profile was carved out in a way that you were in alignment, then it would distribute your weight across the sleeping surface and in that sleeping position you would have good alignment and pressure relief ... but when you change position you may no longer be in neutral alignment or may experience pressure points.
There is of course a range in each category (wool, horsehair, and memory foam offer minimal amounts of pushback) so it is not absolute. Active or passive is basically determined by two characteristics. One is how progressive the support is in the material (called support factor or compression modulus or spring rate in an innerspring) and the second is how much the material bounces back (called resilience). It is also called "pushback". Other areas of this website talk about support factor/compression modulus and resilience but in general the support factor is measured by the difference in weight it takes to compress a material by 65% of its thickness and the weight it takes to compress the same material by 25% of its thickness. This determines how quickly a material becomes firmer with deeper compression and can "stop" the heavier parts of the body from sinking down too far. Resilience is measured by how high a ball bounces when it is dropped on the material. This also tells you how springy a material is and how much energy it absorbs (called Hysteresis). Both of these contribute to a perception of the softness or firmness of a material.
Air cores are used as a support core in a bed since as a comfort layer I think most people would agree it is not too comfortable (sleeping on a bare air mattress is not most people's idea of heaven). So we need to look at it in terms of a support layer rather than a comfort layer (although support layers can add to or subtract from the feeling of comfort of the layers above).
Air is not progressive. It is basically an all or nothing material that is either not compressed at all or is fully compresses with little progression in between the two extremes other than any stretch in the air bladder material itself. It is very soft until the pressure equalizes throughout the air bladder and then it is suddenly very hard. This can be varied somewhat by certain types of two way valves between individual chambers (The SAT bed was an attempt to do this for example) but this then becomes an attempt to reproduce what other materials already do much better. Even airbeds with say 24 chambers only have 24 areas of "individuality". Foam and springs have hundreds/thousands/millions. This transition from very soft to very hard results in the comments you will often see about airbeds that "I just don't like the feeling of sleeping on an air mattress". The "feel" of an abrupt transition from softness to hardness is often uncomfortable for people. Thicker layers of materials above the air bladder is used to compensate for this feeling.
In many airbeds, there is a great deal of material (latex, memory foam) above the air bladders. In this case, most of the support is being handled by the material itself and very little of it by the air bladders. You almost have a complete mattress on top of air bladders. In this case it would be legitimate to question the point of the air bladders at all. It is like some "modern" innerspring mattresses that often have so much active material above the springs (as opposed to more passive stuffing) that the springs themselves become almost irrelevant.
Progressive support is also inherently better at keeping the spine aligned, especially with changing positions. It does not have a "boundary" where compression suddenly stops. In effect, progressive support is already a form of zoning that can be enhanced with the zoning that is often being added to mattresses these days. What this added zoning does is change the "range" of support levels that are already inherent in different materials and support methods. This means that if the spine is aligned in one position, it can also offer support/alignment in a different position that requires it to sink in more (changing from back to side for example). This would often require an adjustment in an air bladder, especially if you have thinner top layers over it. Even very cold or very warm memory foam is more progressive than an air bladder (talking about progression here not softness).
The idea of resilience or pushback in varying degrees is that it can offer better support to the "more recessed" areas of the body (small of the back when you are on your back and waist when you are on your side). In more passive materials without resilience, the spinal alignment and support you have once you stop sinking in is what you are stuck with. If it's perfect, then you have it made, but what about when you change position. Even a material that "perfectly" conforms to the body and offers "great" pressure relief (such as memory foam or buckling column gel) may offer that pressure relief with the spine completely out of alignment (sleeping in a bow or an arc). Pushback or resilience (in combination with progressive support) allows the support layers of a mattress to keep the spine in alignment in many different positions and provides underlying support to the more recessed areas of the body (small of the back when lying on the back or waist when lying on the side etc). This is one of the key areas of bed design and is why you see so much research into "response curves" and "zoning schemes". It is also part of why different designs work for different people ... most of whom move into different positions when they are sleeping.
An air bladder has very little resilience. What this means is that unless you require the same levels of support in all of your sleeping positions, you will need to adjust your settings when you change from certain positions into other positions that have very different profiles and support needs. Even the attempts to compensate for this still are not as successful as what other support methods do more naturally.
It seems to me that an air bladder ... even one with many individual degrees of adjustability ... is a costly way to do what other materials and methods do more effectively, with more variability, and at a lower cost. An air bladder with 100 different support settings is competing with support methods (that have progressive support and resilience) that have thousands if not millions of degrees of microadjustability ... and this adjustability is automatic and doesn't require a manual adjustment. An air bladder with several zones of support on each side is competing with materials that through their comfort factor, resilience, and zoning schemes have thousands and millions of microzones.
One thing that I will say for an airbed is that for those that have individual zones with separately adjustable firmness settings for the center third of the mattress (which I would consider to be an important option in an airbed to offset the sagging that can happen under the hips/pelvis on softer settings) then the range of firmness (the airbed equivalent of ILD) between the zones can be greater than other types of zoning that you will commonly find and the middle of a mattress can be set to firmer levels and control how much the heavier parts of your body sink in relative to the zones in the upper and lower parts of the mattress (under the shoulders in particular) which can improve alignment. This type of more extreme differential though would only be necessary in more difficult circumstances or with more challenging body types and can be accomplished in other ways as well in other types of mattresses that have a zoned construction (engineering different zones with foams that have much different ILD's for example) using materials that don't have the inherent weaknesses of low compression modulus combined with low resiliency.
In a limited trial in a store you may find a setting that feels comfortable even with thinner comfort layers on top but how comfortable it will be when you get it home and it is exposed to the real world of your changing comfort and support needs over many nights and years is open to question. You may also find an airbed with thicker more active layers on top that feels wonderful in the store and feels wonderful when you get it home and sleep on it for a longer time but how much of that "perfection" are you crediting to the air bladder and how much of it is really coming from the thicker layers on top.
Granted it may take some research and effort to find a more "traditional bed" that has the comfort range (ability to relieve pressure in different positions) and the support range (ability to keep the spine aligned in different positions) that fits you but once you find this you have a mattress that adapts more naturally and "automatically" with thousands/millions of variations in support instead of 20 - 100 and thousands/millions of variations in microzoning instead of a few (usually 2 or 3) areas of individual macro zoning on each side.
Mechanical breakdown, leakage, mold issues, breathability, durability, noise, middle dividers, and ease of use are all issues that come up with airbeds and while they have been dealt with to varying degrees by different manufacturers, they are not all completely solved. Complex mechanical systems as a whole have issues that are not inherent in materials that do not need "mechanics" to function.
Having said all that, if you are looking seriously at an airbed, then there are many manufacturers that within the limitations of the system itself are producing airbed mattresses that have greater value and more features than the top 2 manufacturers (IMO). It may be surprising how many there are and the huge variability in prices may be more surprising yet. More expensive and even much much more expensive in airbeds doesn't always translate into better quality materials or better value. Take a close look at how much you are paying for a name, how much you are paying for the air bladder system, and how much you are paying for the quality of the materials above the air bladder system. Compare the features and construction of the air bladder system. Compare air bladder systems with similar comfort layers and similar features and quality to each other, and compare the zoning options and the side by side split options and you may be very surprised at the significant discrepancies in prices and features and value.
As in anything else, there may be some people for whom an air bladder support system is absolute perfection and are quite happy with the price they paid for it. They also have the advantage of other component mattress systems where the individual layers and components can be replaced individually rather than having to replace the complete mattress. Overall though ... I would make some very careful comparisons with other types of mattresses based on real world performance and benefits outside of "marketing" information and would question their value when compared to the alternatives.