Even in cases where it cannot be definitely proven that any such abuse has taken place, the Church has still wound up shelling out millions in out of court settlements. This actually drove several parishes into bankruptcy.
It's also worth noting that many of the priests being branded as "pedophiles" here were actually simply homosexuals who went after (often sexually confused) men who happened to be younger than 18. Given how understanding of both genuine pedophilia and homosexuality were in their infancy at the time most of these events took place, it was sometimes viewed as being sufficient to simply transfer a priest to a new area, and have them "pray the sin away" in an effort to reform and rehabilitate themselves.
Granted, that was clearly the wrong call. However, that being said, you're ultimately blowing the problem out of proportion.
The Church never had any more of an issue with sexual abuse than any other institution, either religious or secular. The abuse rate was actually lower than that found in the general population even at its worst. It's response to the abuse it did find also wasn't any different than what most other organizations at the time did.
Society as a whole was somewhat messed up on this particular issue. The Church simply happens to be an easier target to go after than most.