I was with you right up to this point:

It would be a good idea for psychological profiles to be added to background checks

I don't like that idea. The last thing we want is for people to be punished for things some test says they might some day do. I don't want to live in a "Minority Report" society. I preffer that people be judged by the things they've actually done and the way they actually conduct themselves, not by what a test says they might some day do.

I agree with the rest of your post. This is exactly the kind of thing we need. Parents should be relying more on these networks of trust than on a government registry. Nothing will ever stop child sexual abuse 100%, but these types of things are what can lower the rate as much as possible.