I have thought about this a fair amount. I feel quite certain that if no adult engaged in sexual activity with a child without prior written consent of all parents/guardians, sexual abuse would be dramatically reduced. I would certainly urge any pedophile who is inclined to ignore the law to at least get parental permission -- I think in practice it will be denied the vast majority of the time.

I think you may be surprised by the social change this would likely begin and how many parents would allow it, I also think you would be surprised, in a more sexually relaxed society, how many kids would be seeking such activities with adults. Kids aren't thinking along the lines of "oh hot damn he is sexy and gets me all hot" but more along the lines of "I like him, this is fun, it feels good, I want to make him feel good". It's more playful in nature and about pleasure and being together.

However more important is that in such a society researchers could actually research the effects of consensual adult/child sexual contact. Which is near impossible currently.

Dangers include parents who do not care, do not understand future risks, or parents who give permission as part of a quid pro quo -- some version of prostitution.

And they would be few and far between though no doubt the religious and hysterical would scream these cases from the mountain tops if the law were relaxed in a way I suggest.

I could imagine an age of consent of 14 provided it is with parental permission, 16 otherwise, though I would want to hear arguments from reasonable sex-positive people who are opposed to it.

Yes, but I was talking about prepubescent children and parental consent. Age of consent already is 14 or 15 in some developed nations. They have no big problems. It was 14 in Canada until a few years ago.