Most people are fine with hot tubs aka spas, which are essentially this. (In fact most spa designs don't even filter all the water on each re-circulation, as th

Most people are fine with hot tubs aka spas, which are essentially this. (In fact most spa designs don't even filter all the water on each re-circulation, as there are returns both at the bottom and in the skimmer, and only the latter is filtered.) Re-circulating shower sounds like a great idea to me.