Yep, the celibacy is not about sex but about marriage; throughout history it was not that rare for priests to have unofficial spouses and kids, and at some times it wasn't even particularly shunned, but the concept of celibacy ensured that there couldn't be any legitimate kids i.e. heirs.

Also: it is pretty much only the Catholic church that mandates celibacy for priests. The Eastern churches allow married priests, but not bishops - while one tenet of Protestantism is the priesthood of all believers, where everyone should be able to talk with God and play a role in church affairs.