[Heliand]

This prohibition on marriage, first universally imposed on clerics and monastics by the First Lateran Council of 1123

Was this before or after Pope St. Siricius reiterated the law of celibacy to his clerics in the 4th century AD? I'm a little confused about the timeline you are trying to portray. I think the 4th century AD is before the 12th century AD, but your very absolute statement that it was first universally imposed in the 12th century means that the 4th century must have come after the 12th century. Right?

[Anti-Utopian]

That is a different law that refers to married bishops, priests, and deacons with children, who upon ordaination were required to no longer have sexual relations with wives to remain pure for altar-work. Siricius was angry that clergy were ignoring this rule and continuing to romance their wives and father children.