Hi viva_dc,
There is certainly “some” truth to this and latex can oxidize with exposure to air/oxygen/ozone, and ultraviolet light along with some of the other substances that are listed here. The type of cover can affect how quickly latex oxidizes but it’s not just a black and white or “good and bad” comparison because there are also other tradeoffs involved and some people prefer to sleep more directly on the latex and others do best with a cover that is quilted with various materials or fibers. In general though it’s correct that thinner covers can affect the oxidation of latex more and you can see some examples of this in post #3 here and in post #3 here. For those that do decide that a thinner stretch knit cover is their preference then I would at least make sure that it is designed for use as a mattress cover and not just a very thin cover that will wear down and become thinner or threadbare more quickly and potentially have an even bigger effect on the oxidation of the latex.
I would also be aware that an expectation of a mattress lasting 15 years may not be realistic because especially with children that are still growing their needs and preferences may change over time faster than that even if the mattress is still in good condition. Of course with a component latex mattress you can always add an additional layer or replace layers instead of replacing the entire mattress if that ends up being necessary.
Phoenix