Well, no, it doesn't, and its important to note what the actual bans are to understand why it doesn't. There is:
* a fairly hard ban (essentially absolute, except for an exception noted at the end of this list) on men who are already priests marrying in the Catholic Church,
* a softer ban on married men becoming priests in the Latin Rite of the Catholic Church (this is the 12th Century rule you reference),
* no ban on married men becoming priests in the Eastern Rites of the Catholic Church,
* a fairly hard ban (essentially absolute, except for an exception noted at the end of this list) on currently-married men becoming bishops in the Catholic Church,
* no ban on men who are widowers (including men admitted to the priesthood while married) becoming bishops in the Catholic Church,
* no ban on a married Catholic man (possibly a layman, a Latin Rite deacon, one of the already exceptional Latin Rite priests, or an Eastern Rite priest) being ordained Bishop of Rome after being elected by the College of Cardinals (the rule for this specific allows any Catholic man to be elected) to the Papacy, though its never happened.
It is not impossible for a man to be both married and have children licitly while being a Catholic priest, and it is not impossible for a man to licitly have children through marriage as a widower while being a Catholic bishop (including the Pope), and its even technically possible for a married man with children to be Pope, though it is improbable that someone not already a bishop---and therefore not currently married, but possibly widowed and with children—and cardinal would be elected.)
As I said originally, there is no rule against a Catholic priest having children, though “there are a number of other rules which can combine to make it look approximately like there is.”
That was the theme of the third "act" of one of my favorite novels, 1978's The Vicar of Christ by Walter F. Murphy.
Act 1: The protagonist — a young Catholic, son of a U.S. diplomat, and U.S. Marine Corps junior officer, is wounded at Iwo Jima in WWII. After becoming a law professor, he's recalled to active duty for the Korean War, where he's awarded the Medal of Honor for valor as a battalion commander in combat. (The author was himself a decorated Marine officer in Korea.)
Act 2: Years later, the protagonist is a longtime law school dean. He's appointed Chief Justice of the United States because of political deal-making between the President and a couple of different senators who have agendas.
Years after that, after a personal tragedy, the protagonist resigns and joins a monastery.
Act 3: Having been a monk for just a couple of years, the protagonist is elected pope by the College of Cardinals as a compromise candidate after a long deadlock between the two front-runners. He takes the name "Francis" (after Francis of Assisi) and immediately begins shaking things up both institutionally and doctrinally — to the displeasure of traditionalists.
