Dany only came to Westeros in this season, and as Messandei pointed out, what she accomplished in Essos and nothing to do with her last name. When she came to Westeros she did so knowing full well that the Iron Throne has to be won through conquest. Birthright doesn't matter. The person sitting on the throne right now, had their husband smash the Targaryen birthright to it. Right by conquest is the way to take back that throne.
What I'm asking is, even with Sam and Bran wanting to get Jon to take the throne, how does he do it with just the North and the Vale? A second Targaryen claimant to the throne isn't going to pursue Cersei to give up the throne. On top of that, forget Dany's reaction, what's the North's reaction going to be when they find out that the man they though was Ned Stark's son, is in fact the son of the man who they lost thousands fighting against? Lord Glover is already miffed about Jon's rule, and Lord Royce hates Targaryens. Something tells me that there is where the majority of your human v human conflict in the north would stem from.