There is nothing wrong with rubber banding your feet, so long as it is done for the correct reason.
For myself, I use rubber bands for competition barrel runs when money is on the line. I didn't start wearing rubber bands until I was about 17 or 18. I very rarely lose a stirrup. Ever. But on a couple of those rare occasions, it was during a competition run. I don't want to have to waste any time trying to get my stirrup back when the winner is determined by thousands of a second, and I also don't want my lost stirrup to cause a change in my body position that might affect my horse's performance. Rubber bands are cheap "insurance" to make sure you don't lose a stirrup during competition.
I only use the very thin and very large rubber bands. Often, they break simply when I try to put them on or off, so I know they will break in the event of a fall.
Rubber bands should NOT be worn if you frequently lose a stirrup. If you frequently lose your stirrup, then something else is going wrong in your body position or leg position. The rubber band should only be used as "insurance" and not as a crutch.
As far as kids, I learned how to ride without them FIRST and so that would be my stance on rubber bands for kids. I will not let my own (future) children wear rubber bands until they are at least teenagers and have a good seat and good legs. Now, that could be swayed a little bit, say, for a 9-year-old riding for the NBHA World Youth National Championship, as an example. But as a general rule, I would say no rubber bands on kids so that they learn on their own how to keep their stirrups.
Everyone kinda does their rubber bands a little different. Here's on example: (I myself use rubber bands that are thinner than these.)