Airlines lavs are no different from any public bathrooms out there, trains, restaurants, hotel lobbies, etc. Would you go with your bare feet in any public bathrooms (provided if folks stop peeing on the floor)?

I don't remember seeing anyone going to the bathroom without anything on their feet other than in the airplanes. Why? Airlines lavs are not cleaner than others. Unless you fly SQ (may be NH sometimes), the Singapore girls clean the lavs in C and F frequently during flights. Even on SQ, I'd wear something on my feet before entering.