The reason why I think it is okay for sneakers to be worn without socks is that lots of people already do it anyway, especially women. Women wear flats, moccasins, TOMS, pumps, and slip-ons, all without socks. All of them are closed-toe. That's not all, though. They do wear like actual sneakers without socks.
It is really really gross and then your feet start to smell and then everbody gets mad cause your fett smell really bad. Also you can get really bad blister and foot fungus. It is just a bad situation. I would reccomoend very strongly to wear socks when you wear sneakers.