We tried an absorbent type of bathmat. They were cute but felt gross under your feet when they were wet. Everyone thought they were unsanitary.
We tried using normal towels, but that only works for the first person who showers. After that it’s just a nasty wet towel on the floor that people don’t want to step on. It's not worth the hassle of replacing them or the expense of washing them.
Some hostels have used wooden bathmats. They look great when they’re new, but I have heard that they are really hard to maintain. I haven’t tried them myself but recently saw a place that used them. They said they get slippery and they bleach out after repeated sanitizing. If they’re not cleaned often enough they can grow mold easily.
I used to work in a veterinary clinic, and we used simple plastic mats when we washed the dogs. They aren’t the prettiest things in the word, but they could be worse. Plus they are easy to spray down with a disinfectant to clean without bleaching too badly. I’m not sure if these are the same plastic kitchen mats you’re describing. They definitely would not dry anyone’s feet. The ones I’m thinking of look something like this:
Currently we don’t use a mat, but keep a mop handy to wipe away the drops. A big squeegee works too if your floors aren’t textured.