I also can't wear any sort of slipper without a back. I don't really like shoes without backs either. I struggle to keep them on my feet (even flip-flops).

I usually wear socks with rubber grips on the bottom in the house--lots of hardwood steps (townhouse). I slipped and fell while rushing down the stairs in regular socks years ago, so I avoid regular socks without shoes in the house. I have started wearing some house shoes at times, as I think walking on hardwood is now hurting my ankles and feet.