Don’t have time to track down a “long list,” but here are three obvious and famous examples:
Eleanor of Acquitaine, who “annulled” her marriage to the King of France and married the King of England. I’m unsure why the French King let her get away, since she took about half his kingdom with her.
Henry IV of France, who annulled his marriage to his childless first wife so he could marry Catherine de Medici. He had lots of leverage with the Pope because he’d recently converted to Catholicism and could obviously convert back if thwarted.
Louis VII of France, who annulled his marriage to his first wife in order to marry the Queen dowager so he could retain control of Brittany. This was considered particularly seamy even at the time. The Pope in this case was Alexander Borgia, who even most Catholic historians recognize was not exactly a shining star of probity.
There many, many more. During the Middle Ages the Church was by necessity as much a political as a religious institution, and political necessities, such as the need for a male heir, were taken very seriously. Especially if the king contributed large sums of money to the Pope and cardinals.
They were too closely related by blood. This still applies today.
Henry IV of France
As a Protestant who was in a common law marriage with the same mistress both before and after his marriage to Margaret, he clearly was not in a Catholic marriage with her.
Louis VII of France
He was forced, before he reached the age of consent, by his cousin who - as king - held the power of life and death over him, to marry an eleven year old girl so his cousin could cement his own power.
There many, many more.
Apparently not, since of the three you came up with, two are very clearly legitimate cases of annulment. Henry IV didn't even pretend to be serious about his marriage and Louis VII was clearly coerced.
These are clearly not your "happily married for 20 years with kids until one party wanted out" stories.
Eleanor's case is less sympathetic, but consanguinity was a known impediment to marriage and she ignored it. Rather than the Church inventing a loophole for her, she deliberately entered into an impeded marriage knowing that she could demand an annulment and the Church would have to give it to her, since the law of consanguinity was not ambiguous.
That should be Louis XII whose annulment was granted by Alexander VI (the Borgia pope). Louis VII was king in the 12th century (he took part in the Second Crusade) and had his marriage to Eleanor of Aquitaine annulled.