Rhaegar's annulment: Robert, Robb, or Randyll?

Here are the reasons I can see why Rhaegar would get an annulment, and how those reasons parallel other ill-fated R characters:

1. Elia cheated on him and he was not the father of Aegon 1 and Rhaenys. This is similar to what happened to Robert, except Rhaegar found out before his death. I don't see much evidence to support this (no bad stories about Elia, just bad health).

2. He was motivated only by his love for Lyanna. This is most like Robb's story: making a politically stupid alliance because of love. It's worse for Rhaegar, though, because Robb just broke an engagement to some unspecified Frey girl. Rhaegar set aside his kids and their mother for love of another woman.

3. He thought a legitimate targaryen baby with Lyanna would fulfill the prince who was promised prophecy. If this is the case, he's not much better than Sam's dad, who cast him aside for a younger son whom he liked better (exept Aegon 1 actually ended up dead when his dad dumped him, while Sam's tenure with the Night's Watch has made him stronger).