Occasionally some people suggest shoe covers as an alternative to shoe-removal.
I have expressed scepticism before that shoe covers can be worn with high heeled shoes. I find it impossible to imagine what an high-heeled shoe with a cover on would look like. Shirley Saunders supports my suspicion. She points out in her book that shoe covers can be damaged by high heeled shoes.
From an aesthetic point of view, I would not want people walking about my home in covered shoes. I want it to be a place of relaxation not a crime scene. In any case, I think most people would feel sillier and more self-conscious in shoe covers than in socks or bare feet.