I want to wade in here and provide some additional context. As background, I'm finishing up my BSc in Wildlife Biology this year, and have participated in numerous federally and state permitted avian research projects, most involving banding.
I can assure you that the banding projects I've been involved in take the welfare of the animals as the first and foremost priority - we have extensive training requirements for those handling the birds, strict environmental conditions for when we have to shut down the operation for bird safety, anti-predatory measures. For example, during on Saw-whet owl banding season we heard a Barred Owl calling near our nets, and as they could potentially prey on Saw-whets, we posted a guard sitting silently in the dark next to the nets on rotating 30-minute watches for 7 days just to ensure that if a Barred Owl showed up and tried to get an owl in the net we would be able to take action. I've never experienced "hobby" banders as previously alluded to, and I be very surprised if you ran into such a situation. In an analysis of banding injuries, out of ~621,000 banding encounters, ~0.23% ended in mortality (Spotswood et. al, 2012)
These precautions and requirements are even more strict when Threatened & Endangered species involved. I spent a season work on a T&E crew monitoring Piping Plover populations, and as a part of our permit from USFWS we were permitted 5 "incidental takes" for the entire season along the entire project (~1000 miles of river across dozens of field crews). Meaning that if by whatever means 5 adults, juveniles, or even eggs were killed or destroyed along the entire project, all work had to stop every where until the supervising biologists were able to assess the situation and give guidance on how to proceed. This stuff is taken extremely seriously.
As for why we band, there are numerous reasons. Primarily is it provides a wealth of demographic data. Every bird is aged, sexed, body condition recorded, physical measurements, etc. Often a feather will be taken for genetic analysis if that will be useful for the study. As part of this, every bird is banded with USGS aluminum bands - that's your standard ID band with a unique number. Depending on the study, unique identifiers may be applied as well like colored bands for easy individual ID during resighting studies. Its far easier to see Yellow over Metal/Blue over White than trying to read the silver band numbers. In other cases like condors, wing tags may be used. And as seen in the spark of this conversation, data loggers and transmitters may be used.
Someone above linked to a video about MOTUS tracking, which is something I've worked with a fair bit - it is one of the most exciting new technologies for tracking fine scale movements of birds, aiding in our understanding of migration routes and timing, but again, it requires capturing birds to attach the MOTUS backpacks to them. It's a necessary evil if we want to understand how birds are responding to a rapidly changing world.
In an ideal world, we would love to not have to handle wildlife - that's what's safest for them and for us, but many of the questions we want to answer simply can't be evaluated right now without the use of tagging of some sort.
1. Spotswood, E.N., Goodman, K.R., Carlisle, J., Cormier, R.L., Humple, D.L., Rousseau, J., Guers, S.L. and Barton, G.G. (2012), How safe is mist netting? evaluating the risk of injury and mortality to birds. Methods in Ecology and Evolution, 3: 29-38.
https://doi.org/10.1111/j.2041-210X.2011.00123.x