Many cases will be like that yes. And if, as they say, the databases are limited to wanted persons or convicted felons, then the priors won't be terribly out of whack. But it's going to be way easier, PR-wise, to broaden a face database than it ever would have been to broaden a DNA database. It did not take long in the UK, for example, for the National DNA database to creep from "only convicted criminals" to "anyone arrested, even if they were never charged".
And that's with people's DNA, which is pretty invasive to obtain. The government takes routinely takes pictures of people; there's no visceral moment of privacy invasion there. It would be easy for the database to expand to include a tremendous number of people, and then your false positive rate really is a problem. It stops even being a reliable way to narrow people down, because there just isn't that much variance in human faces, especially if you have to deal with low resolution and/or noisy data.
And that's with people's DNA, which is pretty invasive to obtain. The government takes routinely takes pictures of people; there's no visceral moment of privacy invasion there. It would be easy for the database to expand to include a tremendous number of people, and then your false positive rate really is a problem. It stops even being a reliable way to narrow people down, because there just isn't that much variance in human faces, especially if you have to deal with low resolution and/or noisy data.