You already have to take water anyways even if you take regular wet wipes, and you should already be taking some extra water just in case. You don’t need as much water for these towels as wet wipes use, and in a lot of cases you can use water from the environment (like a river/stream/lake/rain/etc) so long as you’re not ingesting it or putting it on wounds, say if you’re using it to keep cool or clean yourself. You can also use excess water from what you already use for other stuff like if you’re washing dishes or washing your hands and so on. So you don’t really have to take more water than you would have anyway. Some hiking trails provide occasional stations with potable water as well, at least where I live, particularly if they’re near/around a campground.
Usually you’d have a bag for garbage that you can put it in. It mainly saves space to start with in your pack. You have other supplies like food and water which will be used up over the course of the hike, providing more space on the way back that wouldn’t be there at the start, so the towels expanding after use isn’t as much of a problem.
If you used it to wipe up a spill you wouldn’t have to wet it first, just throw it on the spill and it’ll soak up the liquid, then when it starts expanding from that you can use it to wipe more thoroughly.
Watching mouths fill up with towels (lemmy.world)