You keep saying he doesn't care about being king as if that is some prerequisite for being king. The show's thesis, as presented this season, is a king that doesn't want it. Bran said he doesn't want anymore. That means he doesn't have the blind spots of past rulers, or crippling devotion to love, or anger and vengeance of past rulers. He has the wisdom of every king that has ever existed and will only make practical decisions that benefit the realm, not to serve his own interests. Bran the broken becomes Bran the rebuilder, a god-king.
I fully believe that comes directly from GRRM, too.
So we let Jon refuse the throne because he doesn't want it. Even though the show has made it a thing to continue to put him in a leadership role since season 2 no matter how much he thinks he doesn't deserves (or desires) it.
But Bran, who since day 1 was fukked out of that kind of position and had an multiple season journey to become the 3 Eye Raven, is suddenly like "OK, FINE I'LL DO IT" after saying this entire season he has no business doing any of the sort. And that makes sense?
I understand that in theory, Bran could be a dope leader. But the show has shown NONE of that and made it a thing to continue to tell us he's not a part of the politics game anymore. It makes sense that people from Westeros think he could be a good King/ruler, it doesn't make any sense that Bran would actually accept it. Not because he couldn't pull it off, but because nothing that has been established on the series makes it believable he would accept that kind of offer.
And the last king that didn't want to be one was Robert, and look how that turned out. Varys saying "well maybe that's the formula" is awful writing coming from him.