We place removable bands on dogs, cats and sometimes horse: collars. Easier to have them brought home when they are found, same with bands on birds. I mean, cows have a tag attached to their ear, like a piercing, and they do a lot more damage than a ring on a leg when things get caught on themWhile this info is indeed important, it does not need to be carried on the bird.
My Avian Vet has seen bands severely damage birds. IMO- its a better idea to remove them, and keep them safely somewhere perhaps in a file with the vet records. If they have to be re-homed they go with the bird. Just like dogs, cats, horses. Why don't we place bands on dogs and cats?? Because its not very humane. Nor is it on birds. My Ki sometimes bites his, and sometimes it seems to irritate him, I can tell he doesn't like it. We're having it removed like our vet suggested.
As for sending it with a bird when it's rehomed, how many people can you see doing that? Some birds are cheap so anyone can get their hands on them, they are going to bother holding onto a band for a ornament they have in a round cage with a swing. For rescues, the band is probably a good thing, it's easier to place the poor homeless birds when the age is know ):
I'm not saying I like them, neither of my birds have bands, I don't like them. I'm just giving some an idea of the other side of the argument personally, I'd like to see microchips become bigger for all animals and for it to be normal for anyone to have a scanner, I can imagine that being a whole lot more comfortable!