When I was a kid, I recall police coming to our classrooms to fingerprint us. The whole school got fingerprinted. The idea was to help police if kids went missing.

Whether or not you believe that justification ("Stranger Danger" was a scare at the time), I can promise you those fingerprints were used to put people in jail later.

I think that's a bit safer, because you could deduce very private information from a DNA sample, but you can't really tell anything about a person from their fingerprints, except maybe the size of their fingers. It's a one way match