You really DO want to wear good sturdy shoes on an airplane during takeoff/landing as that is the most dangerous part of the flight. In the event of a crash and you do survive and your shoes have not been knocked off, your shoes will come in handy to step over sharp debris etc exiting.
Now for cruising I always take my shoes off and wear socks at my seat. When going to the toilet, I always put my shoes on. Say hello to germs and who knows what in an aircraft toilet.
Bare feet on a public aircraft: GROSS........ Unless you enjoy foot and nail fungus.