While it is true that government databases identifying the DNA of every citizen would reduce crime and increase convictions, it also means a great many other things. Here are two of them.
1.) Police would get very lazy very quickly. DNA would be used as the "de-facto" proof of guilt, in spite of the fact that DNA is shed by everyone all the time. An ex boyfriend gets accused of rape and since his DNA is there he's automatically guilty. A store gets robbed and the man who hasn't bathed in a week gets charged because his DNA is the "most prevalent" around the register. He probably should have used Dial.
2.) Just because our government is mostly benign now doesn't mean it will always be that way. When social and economic upheaval occurs a great many things can change. Imagine, if you will, a government run by neo Nazis. Suddenly they have DNA proof of, not only the Semitic groups, but all of their offshoot genetic cousins as well. Or perhaps someone develops a gene targeted disease and gets their hands on the government database. for my closing, one word: Gattica.
As to the man accused of rape in the Netherlands, I am curious if he was just trying to play innocent, trying to turn himself in, had forgotten about the rape, didn't think of the incident as rape at all, or if he is innocent and somehow got his DNA involved through some other means than direct collection from the victim. After all, it does seem a bit moronic to give one's DNA if one has committed rape (or any other crime) and hasn't been caught.