If you read the book, which I think is available online, see the link, you will realize that non homosexual men or men not supportive of homosexuality were rejected from the priest hood in many districts.
The CC did not permit a rejected applicant to apply in a different district. Rose speaks a lot about Boston District IIRC.
All I’ve ever heard is that the church doesn’t have enough priests. Parishes in my town share priests because there aren’t enough to go around. And they’ve been turning applicants down?