Bathrooms should have a floor drain regardless of whether they are of the wet variety. I personally hate the concept of a wet bathroom and the behaviour it encourages. Stuff gets wet that shouldn't, it just makes everything harder and expands the scope of cleaning while compromising "dry" tasks after someone else has used the shower if they partake in the undisciplined behaviour the design encourages. Also not a fan of all the functions being in one room.

No you don't touch the towel to the shower floor, you do everything but that. Then you step into the mat mostly dry, not cold, not making a mess to finish.

...lift up your feet.