As to your questions, as far as I know, nobody has ever been murdered in a place where I've been. Maybe on the sidewalk somewhere, but that is not a scenario where DNA is going to be any help, unless the perpetrator leaves behind blood or skin on the victim or the ground. And I've never had sexual contact with anyone who was subsequently raped, nor anyone who didn't already know me for that matter. But it hardly matters whether those things have happened to me personally. What matters is how often that happens in the world, and what fraction of the time this leads to incorrect prosecution.
That depends[1] strongly on what question you are asking. Matching an unknown sample against a small number of suspects is a very different question than searching a database with millions (or billions) of records. The latter is almost guaranteed[2] to return false positives.
> it massively improves the odds of finding criminals
That's a strong claim that requires equally strong evidence.
[1] https://www.schneier.com/blog/archives/2008/09/dna_matching_... ( http://archive.li/M0SeV )
That's awful wishful thinking. The general public is of the opinion that DNA evidence is 100% accurate and the government does a great job of continuing to present that farce. I wouldn't want to be the person who has to face a jury of their peers in the face of DNA evidence saying I committed a crime. Regardless of my alibi... I wouldn't trust the lay person to understand or get it right.
I'll bet X gets convicted.
There’s a temptation to compute “1 in a billion” probabilities, have a computer or science wizard process spit them out and for investigators to conclude the person who matches is the one. I’m more worried about the possible lazy or sloppy interpretation and curve-fitting aspects of the tech than I am worried about me flipping out and committing a felony offense.
I am likewise glad for the cases where it is helping to correctly solve crimes, of course.