Dany's Vision: Rhaegar

[A rose by any other name]

You can't march off to face your foe on the battlefield and then spirit your family somewhere safe in case you lose. The hit to your soldiers' morale would be severe.

But I'm puzzled as to why people don't think Jon is a bastard. If Rhaegar was married to Elia, then he couldn't father a trueborn child on Lyanna -- at least, not in the eyes of the church and virtually every noble house in Westeros. The only way it could have happened is if the marriage was annulled, which I doubt because someone would have mentioned it by now.

So by definition, Jon was Rhaegar's bastard son, which doesn't mean he (Jon) couldn't become king -- it would just take a Blackfyre-type rebellion to put him there. And Jon can also be a dragon head, since that seems more of a blood/genetics thing than a cultural/heritage thing.

You're overlooking the fact that the Targaryen family has,on multiple occasions, practiced polygamous marriages. It didn't matter what the other houses thought about it because they all bent the knee to them. We don't know if Rhaegar took Lyanna as a wife because we have not been treated to the details of that part of the story. It is certainly a possibility that they were married and that would make Jon legit.