If I use a waterproof membrane, do I have to use tile?
You cannot use redgard or aqua defense as the final coat.  (says this in their product info)  Over time standing on them, dropping things or whatever would cause weak points or holes.  They are meant to have some type of hard surface on top of them for protection - stone, tile, plastic, and so on.

Paint would not help at all.  Any type of paint that got wet would eventually lose binding to the material.  Also paint wouldn't help with the above issues.