The US passport holders get fingerprinted on entry only, as I’ve heard.
I don't care much about "verify that the passport is yours". For centuries, the person presenting the passport was supposed to be the owner of it, with their photo (aka "biometrics") as a proof. Comparing your passport picture with your face is what border controls have been doing since forever.
The fact that we leave fingerprints everywhere is hardly relevant, considering the costs of retrieving and storing them en masse are astronomical.
The licence plates on our cars are out in the open for everyone to see, and yet when a private company collects them and makes a searchable database out of it -- with locations and timestamps -- making it possible for anyone with access to build traceable paths of all of our movements since forever, it results in people getting enraged, and in my opinion justifiably so.