At some time in the past, the FAA had a rule against flying barefoot. All people 5 years and over had to wear shoes while flying. Their rule seems to be gone (a search of their site on 'barefoot' now only turns up an employee living in Barefoot Bay, FL). However, a lot of individual airline companies still have company policies requiring shoes. Other airlines do not. Here are some of my own visions on bare feet, flying, comfort and safety, both in regular situations and in case of an emergency.
Advantages of being barefoot during a regular flight (fortunately, far most of them )
It is comfortable. Many of us who are on this site go barefoot regularly and many of us do it for this simple reason. A long flight is not always comfortable to start with, but being barefoot makes it better.
It is good for your circulation. When sitting in a chair for hours, blood pools in your legs. Taking shoes off and wiggling your toes helps, especially if your shoes are tight but even when they are not. Quite a few sites about the prevention of Deep Vein Thrombosis recommend taking your shoes off while you are seated on long flights.
If you are going to be barefoot in your seat, there is no foot odor if you weren't wearing shoes in the first place. Foot odor is not just 'fresh' sweat; it is sweat being broken down by bacteria in anaerobe circumstances, like inside enclosed shoes. Taking off a pair of stuffy shoes during the flight may cause the people in the next seat to like you far less than they would if you just came in that way.
Good balance in case of sudden turbulence. I know, this is personal, but I have much better balance on my own two feet than when I am wearing shoes. I don't fly much, but I do travel by train very frequently, and when I'm standing up or walking and there is a sudden bump I am much more secure barefoot than the few occasions, in mid-winter, when I am shod.
It is one less place to search when going through security. Okay, a bit a silly reason maybe, but then again, maybe not...
Disadvantages and possible problems during a regular flight:
We might stub a toe. Yup, it can happen. But it isn't a major risk and certainly less than the risk of falling in a moving vehicle, whether plane, train or bus, while wearing high heels, platform shoes or loose slippers/flops. Not that you have any business being out of your seat if there's turbulence, but say we do hit some unexpected turbulence and we were just stretching our legs or going for a bathroom break. We could stumble and hit our toe. Or we could hit any other part of ourselves. The actual damage done if we do stub a toe is hardly likely to be a serious injury, any more than stubbing an elbow on the restroom door, bumping our head on the overhead bin, or getting a paper cut from the inflight magazine. And less serious than a sprained ankle from high heels would be. Also, if they are so worried about stubbed toes, why are most of the rules only for people over five? That is well above the age of kids who are constantly being carried. They're gonna be running around and may be a lot less likely to be careful with all the excitement of the flight. An adult walking calmly from the boarding area to their seat will not be likely to seriously injure their feet that way.
We might offend someone. Well... someone else might be offended by tattoos, spiked hair, piercings, etc, and as long as we don't do actual harm this shouldn't be a reason to exclude anyone.
Advantages during an emergency:
Most emergency slides and rafts for a sea landing do require people to take off their shoes, less time to do so (especially compared to people wearing hiking or combat boots which can be laced up high).
You will have purchase with the toes when scrambling over possible un-even surface or lose debris. I haven't climbed out of any wrecks (obviously :)) but I've climbed over branches off the trail, used my toes when I pulled myself up fences, high shelves, steep grassy banks, etc, etc. Some surfaces can be slippery barefoot, especially mud, but I've noticed on many uneven & steep surfaces that where people with most shoes slip (even with rubber soles like sneakers), I stick like a fly.
Disadvantages and possible problems during an emergency:
Shoes could protect from fire. This one is questionable. I've heard after several of the air disasters in the past years, that the seats/cabin is fire resistant up to a pretty high point, when there might be some smoke but no actual fire. Yet when it goes, it is likely to go in a flash: a ball of fire rolling through the cabin, eating anything in its path. Not something a pair of shoes will really protect against.
Risk of cuts on glass or debris. Yes, possible, but we know glass doesn't jump out and cut our legs off. How disabling is a few pieces of glass or a cut really likely to be? Especially when seen compared to the injuries likely in a crash, and compared to the extra grip you will have using your toes?
Cold. If you're flying from the US to Europe or the other way around, you're flying across Canada and Greenland. (look at a globe instead of a map and you'll see why). This is not a densely-populated area, nor is it likely to be good barefooting weather, especially not in winter. Crash-landing here with bare feet or sandals might well cause a disabling case of frostbite in a very, very short period of time, long before you reach civilization or civilization reaches you. But here again, the sandals are allowed and the bare feet are not, while the sandals would make a difference of, taking a wild guess, maybe two minutes in how long one could walk in those conditions. If you look at the map again, you'll see two minutes isn't likely to get you anywhere in most of Greenland... Nor will many dressy shoes, especially women's dress shoes, do much better. The FAA site recommends wearing low-heeled, canvas or leather shoes for in case of emergencies. If you are worried this seems a lot more sensible than just singling out bare feet and allowing all other types of footwear.