And from what I understand about persecution during the time of Paul's writings, NOT getting married and having a family would be good advice on a practical, as well as "religious", level.
“Yeah—wasn’t the celibacy of priests a late (12th century or so) development in the Church?”
Yep. It was an administrative decision by the Pope. Parishoners were complaining that Priests weren’t doing their jobs because they were too busy working at other jobs to support wives and mistresses. So the Pope said no more marrying.
well, let's first repeat, this is a discipline, not a dogma of faith, so can be changed with no impact to doctrine
But to your point, no, this is not a late development -- at the Council of Elvira in 305 you had Canon 33 It is decided that marriage be altogether prohibited to bishops, priests, and deacons, or to all clerics placed in the ministry, and that they keep away from their wives and not beget children; whoever does this, shall be deprived of the honor of the clerical office. while the council of Carthage was circumspect It is fitting that the holy bishops and priests of God as well as the Levites, i.e. those who are in the service of the divine sacraments, observe perfect continence, so that they may obtain in all simplicity what they are asking from God; what the Apostles taught and what antiquity itself observed, let us also endeavour to keep… It pleases us all that bishop, priest and deacon, guardians of purity, abstain from conjugal intercourse with their wives, so that those who serve at the altar may keep a perfect chastity.
you are right that it became mandatory for Latin-rite only in the 11th century, but since Pope Gregory's time it was recognized as something to be followed.
Among Maronite and eastern Catholics, the rule is that married men can become priests (but not vice-versa)