When the police showed up at his home with an "arrest warrant [that] included a photo that didn’t resemble Bah" they should have immediately figured out something was wrong; that perhaps they've got the wrong guy? As such, they probably shouldn't have followed through with the arrest at all, pending further investigation, unless they had reason to believe the individual - despite not matching the warrant - presented an immediate threat. Which sounds unlikely.
So ISTM that the parties at fault here are (a) whoever fraudulently used his lost ID, thereby falsely associating his identity with criminal activity; and (b) the arresting police who did not pay attention to whether the subject being arrested matched the warrant they had in hand.
But while I am still deeply uncomfortable with the widespread deployment of facial recognition, etc., and would like to see it restrained, I don't see that it's really the problem in this case as reported.
Even if the warrant had looked sufficiently like him to confuse people, it should have been a quick conversation about if he'd lost any ID, what kind, where, and then where he was on certain dates to clarify that he wasn't the thief.
Do US police have to arrest someone to question them?