Given that people shed plenty of blood for our liberties, no, preventing all rapes/murder is not worth surrendering all our liberties.

I.e. I'm not willing to trade away all my liberty for security. A certain level of background crime is acceptable. Just like I accept a certain level of risk every time I get in a car, eat a steak, go jogging, etc.

No, it is not worth it, and in the long-run may not have the desired effect.

For me, after seeing this, I would possibly not report being raped. Arresting the rapist isn't going to directly help me (depending on the situation), so by selfish game theory I shouldn't risk compromising my DNA

Using a rape victim's DNA from her rape kit without consent etc is much more likely to promote rape than to prevent it.

Its a letter of the law versus spirit of the law. I am of the later. Investigating one crime does not inherently give permission to use data from that crime to start trying to solve other crimes unless they are directly connected, i.e. tying a bunch of murders together with similarities because it may be a serial killer instead of one off murders.

I fail to see the preventative aspect. The system really isn't set up for that.

By indexing rape victims DNA?