Interesting idea but if you use "good" fabric, this would wind up being a very expensive bath rug that would be pretty labor intensive to make! And, if you use ugly fabric, it would wind up being a very ugly bath rug!
That said, I've done some wrapped pieces (bowls and trivets) based on the "It's a Wrap" books and they were really fun and "funky". I keep a bag for scrap strips that I use for these projects when I just want a change of pace from other stuff.