I don't know if anyone else will say it, but I think part of the reason is because not every crime deserves a prosecution.
Most murders probably do, but if you have this database you might as well use it for automatic paternity tests too.
Ever spit gum somewhere you shouldn't have? If I was a cop that stepped in gum, with an instant DNA scanner in my pocket, I'd be tempted to scan it and pay the offender a visit.
Laws change very slowly, and things are going to get weird very fast when anyone can run a global DNA scan from their iPhone.