Natural fibers can produce a very high quality and pressure relieving comfort layer in certain circumstances however it usually takes more knowledge and expertise to use them successfully as the method of construction with these materials is as important as the materials themselves. Because natural fibers have less resiliency and elasticity and do not naturally form a pressure relieving cradle in the same way as foam, microcoils, or other materials more commonly used in the comfort layers of a mattress, special construction techniques are needed to use them successfully in a mattress. When these techniques are used, they can produce an exceptional mattress however they tend to be much more expensive than mattresses that don't require the same methods of construction. Natural fibers are used in some of the most expensive mattresses in the world and some of them cost in the tens of thousands of dollars. This is due more to the methods of construction than the materials themselves.
The most common natural fibers used in mattresses are cotton, wool, silk, and horsehair and other animal hairs. There are also some natural fibers that have been or are being developed that are often used as well however because they are among the most durable of materials, natural fibers remain the material of choice in this group. These materials, properly constructed, can last as long as latex and lifetimes of over 20 years in not in any way uncommon. They have different strengths and weaknesses than other materials however and no matter how expensive or durable they may not be appropriate as a comfort layer in certain circumstances.
The first major difference in these materials is that they have little elasticity and resilience and rely on construction methods to give it these qualities. Tufting or "bunching" of the material and attaching it to deeper layers of a mattress is an example of this. This tufting and other construction methods and the use of very high quality fibers can help to somewhat overcome the tendency of all natural fibers to compress and become firmer ... although unlike foams this compression and the impressions it leaves in your mattress is not an indicator of material breakdown and in the case of fibers is even a necessary part of the pressure relieving properties of your mattress. This process of forming a body impression in a natural fiber mattress is called "breaking in" however the mattress industry would like you to believe it also applies to other materials as well which it really doesn't ... at least to any great degree.
One of the strengths of natural fiber comfort layers are their durability and the overall construction of the mattresses which tend to use them. Because they don't easily and quickly form a cradle that shapes itself to the outline of your body, they are dependent on the formation of a more permanent cradle in combination with high quality innersprings which are soft with initial compression to help with pressure relief and then much firmer with deeper compression to help with support. The innersprings used in mattresses like this are typically of the highest quality. As a group have less resiliency than other materials and without a more permanent impression in the mattress, they may not support the more recessed parts of your body as well as other constructions ... again without help from other high quality and resilient layers of the mattress. Some natural fibers do have more resilience than others (horsehair properly made is an example of this) however none of them approach the inherent ability of foam to form a cradle, relieve pressure, and support the recessed areas of your body profile. These qaulities are "given" to them through their construction methods.
Because of these limitations and their need to form more permanent body impressions to relieve pressure, natural fiber comfort layers, especially if they are thicker and not just a thin layer over a very conforming innerspring, may not be as suitable for those who sleep on their side or who sleep in multiple positions as the body impression will relieve pressure to a greater degree in one position than others. While these are not "absolute" statements, they will generally hold true and even the most expensive mattresses made this way ... while there is no denying the quality of their construction ... may not "perform" as well as much lower priced types of mattress constructions in many individual circumstances.
Their other strengths are their very high breathability and temperature regulation, abilities. While this is not connected to the two main functions of a mattress which are pressure relief and alignment, it does play a significant role in overall sleeping comfort and for those who sleep hot and are looking for a mattress which can keep them cool, this may be the answer. They are also very attractive of course to those who prefer either completely natural or organic materials in their mattress as these materials are usually available in organic and genuinely "green" versions (unlike the "greenwashing" claims that are so common elsewhere).
Overall these can be part of some very high quality and comfortable mattresses but real care is needed to make sure that their unique strengths and weaknesses are suitable for your circumstances.