There used to be an ad about a paper towel (kitchen towel) that was said to be so absorbent that, at a pinch, it could be used to towel off after a shower.
(This might be the ad. #include "disclaimer.h" - commercial product.)
I've tried it. Given the right paper towel, it works. It's not as good as a proper towel service, but it's a pretty cheap life hack that does the job. Bonus: it's paper, so in theory at least, it's recyclable.
There are even commercial solutions surrounding single-use towels based on similar principles. (Here's one. #include "disclaimer.h" - commercial product.) I've used these while camping. They are much larger sheets, purpose-designed so probably not a life-hack, but they might be a useful alternative to providing proper towels in a gym.