I think you are mistaken in some details. Monasteries from pretty early on required celibacy. According to https://en.m.wikipedia.org/wiki/Clerical_celibacy_in

I think you are mistaken in some details. Monasteries from pretty early on required celibacy. According to https://en.m.wikipedia.org/wiki/Clerical_celibacy_in_the_Catholic_Church https://en.m.wikipedia.org/wiki/Clerical_celibacy_in_the_Cat..., priests did get married until the 12th century (even then, some say there was an unenforced law rule on the books saying that wasn't supposed to happen) . While there were some theological and worldly reasons for the change, competition with lords wasn't one, and doesn't make a lot of sense. Religious communities were largely populated by the children of the nobles, and nobles gave to monasteries. (And again, wouldn't apply, since only non-monastic priests were married.)