I haven't really worn them down too significantly, but have used 3 different ones excluding a gamecube stick. The newer ones are way better, but each stick tends to have a slightly different resistance pattern, I noticed one was better for playing Caverns agent because it only required a very light touch to the left which made the spiral easier.
I recommend cleaning the bowl and gears as soon as you get one, and I like to lubricate the bowl and stick with graphite powder, preferably taking the time to work it in so it doesn't fall out of the bowl. It might not improve the action of the stick by that much, but it will certainly improve the lifespan of the controller by a good bit. I like to reapply periodically as well. A brand new bowl won't hold the graphite in place well, but one with some scratches and wear will usually benefit. I haven't found any white powder inside after about 2-3 months of playing an hour a day average after using this method.
I have also gotten a loose stick to feel better by using a similar method to Illu's string trick, but using teflon tape around the ball of the stick to make it feel tighter. I can't say if it made the controller better for speedrunning and it didn't last more than a couple months, but it built up the spot where it sat and worked fine.
Ultimately, since the original sticks are crucial to speedrunning, it's worth it to protect them, especially the good ones.