Catholic priestly celibacy was codified at the second Lateran Council in 1139. Before this time there was great diversity in practice in different locations. You had theological justifications for the practice which included Christ's and various apostles' appeals for celibacy as a way of focusing on religious rather than worldly matters. There were also scandals by which large amounts of church property were inherited away from it by priests who had many children which lead directly to a previous decree in the early 11th century by Pope Benedict VIII that the children of priests could not inherit property.

No, there were various theological and practical (inheritance) grounds, I don't think anyone can find evidence for this being an acknowledged purpose. However it could still be an unspoken purpose and it could still work that way. I actually find it very reasonable, given how geeky Catholic priests and monks tend to be, they are prone to typical nerd traits like hair-splitting arguments, they are pretty much like the nerds who can't get some and thus better to rebrand it as a virtue. Just it was not an explicit, outspoken purpose.

I should also say, there were no sexual rejects in the modern sense. Just have a wealthy father, someone will arranged-marry their daughter to you.

The Catholic priesthood is more likely an offshoot of other existing priesthoods from Hellenic traditions and Judaism, some of which were celibate and others of which decidedly not, eg Rabbis are expected to be fruitful and multiply just as much as all Jews.

I doubt it was "invented to do X" -- that implies too much strategy. Instead, I think it happened because of some historical coincidences, and coincidentally it also happened to do X.

The historical reason for not reproducing was the early Christian belief that the end of the world is near, so it does not make sense to marry and have children. (These days there are some Jehovah Wittnesses who don't have children for these reasons.) Of course most people violated this rule and had sex anyway, but following the rule became a voluntary signal of having strong faith.

A few centuries later Catholic Church realized that if they could make non-reproduction of priests mandatory, all resources that those priests would otherwise gather for their families, would now return to the church ownership. And they already had the excuse that not reproducing was a signal of strong faith, so it made sense to demand the signal from the priests. So the Popes began a campaign against marriage of priests; at the beginning the priests ignored them, but gradually the pressure increased, and at some moment one Pope ordered to take all existing wives and children of priests and sell them to slavery. From that moment, Catholic priests were celibate... at least officially, because unofficially I would guess most of them either have a secret wife and secret children, or secret homosexual relations.

Of course the people who are religious and unattractive can rationalize this and join some institution that requires celibate, thus converting their lower status on sexual marketplace to religious status. On the other hand, there are also many attractive people who choose this role because of their strong religious feelings. -- The fact that many priests actually secretly have sex and children is an evidence of their attractivity. Of course there is this confounding factor whether having high religious status could have made the difference in their attractivity. But I anecdotally know about a few people who were considered attractive before they became celibate for religious reasons.