The poster said kids and parents would both wear wristbands, why would adult skaters without any kids present need them? The point is to match up parents and their kids, not to make a fashion statement.
Some Chuck E Cheese restaurants provide matching RFID-enabled wristbands for parents&kids attending parties at the rink, just to ensure that parents don't leave during the party and little ones don't wander outside looking for them. When it's time to leave the party place, the parent-and child(ren) present their wristbands at the exit. The attendant checks to make sure they match before cutting them off so they don't set off the alarm. The CECs that did this were in busy, high traffic shopping centers, ime.
You can tell parents whatever you want, but that doesn't stop some from leaving little kids unattended. Plus, mix ups do happen. I have three kids and I babysat my sister's kids a lot when I was a teenager. It's really easy to have a kid slip away in a crowded place, especially if you're caring for more than one at a time and they have similar colored clothing. Considering what I've seen happen at playgrounds, bracelets are a decent security net to keep everyone on the up-and-up discreetly. I think it's a technology solution to an age-old problem that's far riskier today than ever. I don't think a teenage babysitter is any better or worse. Kids can, and will, get away from supervision. Sometimes, it is a game, sometimes, its just an accident. Look away for 2 secs because one kid got hurt and the other can run off to a part of the rat maze where you can't see them. It happens.
Going with the original theme: Sometimes, little ones want to go skating, but their parents are often unable to skate themselves for a variety of reasons. At my imaginary rink, I would hire a few teenage "skate buddies" who would skate with little ones for a half-hour, not so much as a teacher, but more like a friend. Just holding hands, encouraging and helping them up if they fall. The requirements would be something like the Red Cross Babysitting certification course, just in case the child does get hurt. Beginners would have to wear helmets, gloves and pants.