Possibly for the same reason that my devoutly Protestant mother is annoyed by priests who don't wear clerics all the time. Deep down she's either aware that the Church is what she claims to be (possible) or she's clearly aware that the Church claims to be something that her members don't even believe anymore (probable).
Now this would never be the case for a Freeper Protestant, but there are lots of generic Protestants who turn to Catholic priests when there's something spooky going on and they think they need an exorcist. People expect that members and "officials" of a church that claims to be divinely founded are really going to be "better" than everyone else. Rightly or wrongly that's the way it is. We put "the Church" up on a pedestal and people genuinely expect it to make a difference in our lives...
“the Church claims to be something that her members don’t even believe anymore (probable)”
The vast majority of people that leave the Catholic Church want to live by their rules and not God’s rules. They can’t stand being part of a Church that actually has rules that they should live by. So they find themselves a protestant church that could care less how they live their life. It is not easy being a Catholic, and by that I mean a Catholic that lives their faith. And that is the reason you have people leaving the faith. I have never heard of a devout Catholic that all the sudden left the faith. Devout Catholics would never abandon the Holy Eucharist.