It has to do with professional training and responsibility (duty of care), coupled with kids trusting them more and they are considered to have some para-custodial responsibility for children.

Priests aren’t entirely in that category, but they probably should be, the question is the relationship of the priests, ie a random priest who heard a rumor is very different from one who heard confession or tends the victim or abuser directly.

Also, you don’t want to empower random-ass people too much, people are absolute fucking morons and media will incite them to do something more moronic:

https://www.independent.co.uk/news/uk/this-britain/vigilante-mob-attacks-home-of-paediatrician-710864.html

https://en.wikipedia.org/wiki/Pizzagate_conspiracy_theory

https://en.wikipedia.org/wiki/Blood_libel

Inbred rednecks just danger incarnate, empowering them in any way is insane and will guarantee needess innocent victims.