Also, there is precedent for an heir to a kingdom coming out of order.

By all laws of Westeros, Theon is the only one with a rightful claim to the Iron Islands. Yet when it came time to claim that birthright, it was totally cool for him to pass it on to Yara. And then, despite Yara being Balon's descendant, Euron muscles in and takes over anyway.

So WTF??

And another thing....

Doesn't a successful rebellion kinda destroy any claim you have to the throne whatsoever? I mean, once Robert Baratheon sat in the chair, aren't the Targaryens toast at that point? They could have just killed Aerys and then replaced him with his wife as Queen Regent, with Viserys, or with Rheagar. By all accounts, Rheagar was actually a nice guy. But they didn't. The targaryens were de-throned and Baratheons took over.

If it's a matter of Law, then it seems that the next "rightful" king should be named Lannister. No?

Or, if not, then I still say Gendry has the best claim of anyone on the show