Oil of Wintergreen is a standard treatment for rejuvenating rubber... (Methyl salicylate)Uh, no, you don't, unless the stylus was recently replaced. There's no cartridge ever made where that could be true except perhaps a Decca and that's on account of it having no cantilever. Of course this degradation occurs so slowly that you don't notice if over time. Its only when you get a new cartridge set up properly you realize how degraded the old one got. I've been able to revitalize older cantilevers (if they got stiff rather than collapsing) by using a tiny amount of brake fluid, but that stuff can take paint off so you have to be really careful and patient with it (the cartridge has to lay on its back for a few weeks) to make sure it can't migrate down the cantilever and contaminate the stylus!
IMO this is one of the weaknesses of vinyl; people don't seem to realize that the suspension is ephemeral. I've seen this problem a lot, having put myself through an engineering program by being a service technician- I've worked on literally hundreds of turntables and owned dozens of cartridges.
However - the materials used for the cartridges suspension varied wildly - and so do their response to age
For really good styli, it can absolutely be worth while taking them to a retipper, simply to get the suspension replaced.
I admit, I have not tried to measure the actual compliance of the suspension, to compare to original spec.... something for a future rainy day.