What we need is more pervasive control of discrimination, then, and of other things that could use biometric information.
Simply "hiding" your biometrics or banning biometric identification altogether would be moving backwards in the bigger picture, which I'd compare to forbidding evolution research because it's against religious teaching.
Unfortunately that “control of discrimination” can change uncontrollably in the future so any system we develop now should have some thought to the risks of leaving data which could be abused by a bad actor in the future.
The BackStory podcast had a recent episode on the history of surveillance in America:
Among other topics, one segment discussed how a racist official in Virginia used data collected in the 19th century to protect free African Americans as part of his effort to enforce racial purity laws in the 20th century:
“HELEN ROUNTREE: In the county courthouses, there was another kind of record made, and that was the register of free Negroes. He had to get a certificate stating that they were of free birth, otherwise they could be kidnapped and sold into slavery.
The law about that went in in 1806. Plecker was able to get copies of those registers – every county had one. And then if he got a tip later and he could have his people trace geologically back to a free negro register, he had that present-day person as a person of African ancestry.”
Simply "hiding" your biometrics or banning biometric identification altogether would be moving backwards in the bigger picture, which I'd compare to forbidding evolution research because it's against religious teaching.