I didn't like it when EAA first started this background check. It sure as heck didn't feel right to have to prove you are not a criminal, when we are using our time and some costs to fly dozens, even hundreds of kids. But these are the times we are in, EAA didn't create the problems, they are just trying to keep it out of our organization.
In our small town of about 8000 mostly upscale people, we have had a publicly accused priest who didn't deny it and left town in a hurry. We had a trusted treasurer, not abuse kids, but embezzle from the school art section. We had a child shrink who turned out to not even be licensed and left town in a hurry. He was especially friendly to kids, I never felt right about him. And a school official with a hidden legal judgement against them, noting to do with kids, but not clean either, We had a coach who made it a practice to con money from parents, myself included.

When I was a Scout leader, I made sure to meet at school when I didn't have another parent around since there were teachers and students there after school,

Yes, it would not be normal to have Young Eagles kids alone with in adult at some other airport, but an adult pedophile could likely manage it. How about at some summer aviation event away from public scrutiny? Joe Paterno and Penn St had a good reputation for decades, until someone looked at an assistant.

I don't like it but am willing to put up with it, and the Young Eagle program has been a great success.