Well, then, why stop with just people arrested but not convicted? Let's have EVERYONE submit a DNA sample. And their bank records. And let's allow cops to stop cars and search our homes whenever they want, without a warrant or probable cause. I bet we could REALLY put a bite in crime then.
Have you ever stopped to consider where your train of thought is heading?
I can just as easily make the same equally fallacious slippery slope argument, this time in the opposite direction. Why have law enforcement at all? or government, for that matter? After all, abuses happen, and some of the worst abuses in history are committed by governments.
The truth of the matter is that our choice is not between anarchy and totalitarian government. Some government is good, especially when it is limited to securing the individual rights of its citizens. I see DNA databases as a means to this end, and we can certainly have them while also guarding against potential abuses (in much the same way that we can give policeman guns while making it illegal for them to use these guns for criminal purposes or to commit torts).