Indeed, the government doesn't even need the ID, they ingest a data feed of Passenger Name Records (PNRs) from all airlines. This is why when TSA performs the automated identity proofing, comparing a photo of you to your ID, they don't require that you provide a boarding pass.

Comparing an ephemeral photo taken of you to your government credential at the TSA checkpoint is a temporary formality. At some point, the government credential presentation will be unnecessary.

https://www.cbp.gov/travel/clearing-cbp/passenger-name-recor... (Control-F "What information is collected?")