Yeah. I know. Probably stupid.
That's my pet theory, because I know we aren't going to have a happy ending. I'm not sure how well it matches with the books, but Jon has certainly done everything in the oath even if people consider him not to be held to it anymore. He still seems pretty married to the Watch on TV, though, or at least is paying his child support, so to speak.
In show.... Jon lived and died at his post, obviously. But while he screwed Ygritte and was wildling-married to her, she took him -- he didn't take her. And she never got pregnant. Even in traditional North marriage, it's the woman who is asked if she takes the man. If he hitches with Dany, it could be her taking him, too -- into House Targ presumably.
He calls himself a king, but wears no crown. Sansa is holding Winterfell, and the Knights of the Vale won the glory there. It's going to be most politic if he pursues a relationship with Dany of any type, that he give over any interest "his heirs" would have in the North, besides fighting the dead, to the legitimate Stark bloodline.
There's also the fact Dany's in-book prophecy was she would not bear a living child, and there she has a miscarriage presumably. There are plenty of ways to get pregnant and not actually give birth to a living child. The most likely, given all the hints she's risking her life every time she goes on a mission dragonback, is death doing something only she can do help stop the Night King.
As much as I'd love some epic incestuous dragon culture to remain in Westeros.... I just don't think it's going to happen.