I have a chair that is like that, the armrests specifically which are rarely used but de-laminate over time anyways. The comfort of this chair is the best I've ever owned, so much so that I went through the trouble of tracking down the maker to special order replacements lol. Even though it was out of a little over a year past it's warranty expiration date, they shipped them to me completely for free. These are the kinds of businesses which are really worth supporting and recommending.
Unfortunately that's the thing with most products nowadays. They're all designed to last just a bit past their warranty period. Companies test everything they sell and have a pretty good idea how long each of their products will last under typical usage. Your only options will be to clean it carefully, as in the case of goo build up from your hands, or to replace the rubber piece yourself. You could get someone to lathe a bit of wood (or do it yourself), then wrap foam around that. Insulating pipe foam from the local plumbing depot, similar to the foam grips you can purchase for bicycles, might be one option. I haven't received mine yet (just a few more days!) so I have no idea if this is even possible.
The third option, and the one businesses certainly like the most, is for people to just go out and buy a new one. This is the joy of living in a wasteful world where everything we create is disposable. This is also why I created a small side fund and put a little money into it every month. It inexpensive and builds up faster than you'd think, obviously very useful whenever an emergency comes along.