For the small back yard flock, zip ties work well. I buy a pack of multi colored 4" ties for $1.28 at Walmart! Like anything else, you must use common sense, and do it correctly. I use small pointed nippers to clip the ends, and also to clip the zips when it's time to change up to a larger size. You can clip the tie off simply by clipping through the fastening area, that way, no risk of pinching the bird's leg. The chicks grow so fast that they initially have to be changed after the first or second week, then with decreasing frequency until they are about 5 months old. And no. They can't tighten up on their own. The end is clipped off flush with the little square hole that secures the tie.
https://www.amazon.com/uxcell-Cutting-Spring-Diagonal-Nippers/dp/B00NPZF0IO
I have never had issue with a zip riding up on a bird's leg, getting too tight or otherwise causing any kind of injury. If the owner uses common sense and monitors their birds there should not be an issue.