Steel toes would be really nice if loading weights for the counterweight fly system, but it might be possible to get some strap on ones for this. That can easily break at toe and close down students doing the fly system once the insurance company gets done with your school. Perhaps the school could invest in such a thing as a side thought along with fall protection
etc.
Another good place for steel tips would be if you work in a metals shop part of a scene shop. Steel plate gets heavy. But as Wolf says, in general it's personal choice. People wearing ankle length or longer boots in my opinion are wearing the proper shoes because in addition to what he mentioned, they will with their tough leather prevent the shoe from being cut thru should you drop a knife or scenery on it. They will without steel tips allow your toes to bruse but they probably will not break with a good solid leather boot protecting them even with heavy much less sharp stuff falling on them as will be normal.
One very good reason not to wear sneakers or gym shoes is the above strength, than something that's even more important. A good pair of boots will have a solid sole that will to the most degree possible resist puncture. A sneaker will not. That means that any nails or other sharp objects sticking up will seriously damage your foot if you are not wearing boots at work be it with scenery or lighting. Sharp piece of steel sticking up in the
house lighting area, is just as able to cause you problems as stepping on a nail as a lighting tech.
Just a few thoughts on not wearing gym shoes much less sandles.