Monasteries from pretty early on required celibacy. According to 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.)
On the other hand, bishops must be monks as well as priests, and therefore cannot be married.
2 Now the overseer is to be above reproach, faithful to his wife, temperate, self-controlled, respectable, hospitable, able to teach, 3 not given to drunkenness, not violent but gentle, not quarrelsome, not a lover of money. 4 He must manage his own family well and see that his children obey him, and he must do so in a manner worthy of full[a] respect. 5 (If anyone does not know how to manage his own family, how can he take care of God’s church?)