The Church in the West had to wage a protracted struggle against secular power. Bishops and abbots owned estates, whose income constituted the main support of the Church, but as owners of land the realm, there were constantly pressured to become mere vassals to the king and way too enmeshed with the political nobility. (Look up Investiture Controversy and you will see that reforming popes struggled AGAINST this for centuries.)
If a bishop had sons and daughters, hed be even more deeply caught up in dynastic marriage politics: marrying this daughter to that duke, and this son to that princess, and forming alliances with powerful families for all the political/economic/social benefits that would accrue.
Trying to secure the independence of bishops from the temporal Powers That Be was a huge job, it took a millennium to settle and its not what Id call settled even yet. But, for many centuries in the history of the Church, marriages would have forced priests and, even more so, bishops and abbots, to become even more deeply enmeshed in securing titles of nobility, access to estates and lands, royal alliances and the rest of it for all their children.
The Church was trying to steer clear of that whole web of worldly entanglements. Celibacy --- the avoidance of ongoing dynastic interconnections --- became an honorable way to secure more political independence from temporal power, and hence more freedom to be in this world but not of it.
All good points. The question for the Church today: Are the conditions you described applicable for present day considerations?
There were other reasons that were more tied to popular philosophy than anything, but you hit some good points.