Depending on what people do, the government already has their fingerprints.
Personally, I work around schools so I had to get a background check and fingerprinted for that. I also am licensed to handle explosives, both federally and at the state level. I been fingerprinted for that. I've gone through TSA for hazmat endorsement on a commercial driver's license. That needed fingerprints and a background check.
Getting fingerprinted to get through airport security is the least of my privacy concerns.
But my threat model isn't the TSA. They aren't a concern of mine, although I do opt out of their facial recognition.
I am concerned with internet surveillance, corporate surveillance, and communication surveillance.
Sorry for devil's advocate here because I agree with you but hypothetically the answer would be verification. ie., Google already has your password, so why would they need to ask you for it when you log in?