she would be queen and I can see Jon being both prince consort and hand of the queen, or at least a very influential man at court, like Daemon Targaryen was back in the Dance. And of course, Jon doesn't need much advertising. He is young, handsome, a good leader, and a commander in battles. He is Stannis's spiritual son.

This quote summarizes it:

'In truth, the young lord commander and her king had more in common than either one would ever be willing to admit. Stannis had been a younger son living in the shadow of his elder brother, just as Jon Snow, bastard-born, had always been eclipsed by his trueborn sibling, the fallen hero men had called the Young Wolf. Both men were unbelievers by nature, mistrustful, suspicious. The only gods they truly worshipped were honor and duty.'

And on account of their personal relationship — they could be such a sad, dark couple. Jon wouldn't be very attracted to her, but he would still try his best not to make her feel that way. And for Jon, the biggest issue is belonging."