Wasn't it because litterally everone else who had a better claim to the throne had murdered eachother by that point?
Bran has no claim at all. It is not about "better claim", but "having a claim". Podrick and Hot Pie have about as much claim to the Iron Throne as Bran does. More, in fact, since they live in what remained of the Seven Kingdoms, whereas Bran is from the North.
EDIT: Now that is not to say that electing a member of foreign dynasty as a monarch is impossible - it did happen throughout history - but in this particular case, I do not see
why they would do something like that, especially as Westeros has
no history of elective monarchy. Croatia and Hungary did elect Habsburgs as their rulers, but that is not comparable to this situation as:
1) ruler elected was the Habsburg Emperor,
not a junior member of the family
2)
election of the Emperor meant the personal union with Habsburg lands
3) election was done by more-or-less the entirety of nobility (and even so caused a civil war), as opposed to a handful of assholes with no real claim to... anything, really (oh, and Westerosi "electorate" involved a known traitor)
4) both countries had history of dynasties going extinct and nobility electing rulers - something which in Westeros happened
once, was a consequence of murder and involved an outright civil war, and even so succession was in fact still based on blood ties as opposed to election (Robert got the job not because he was elected but because he was related to Targaryens)
Say, if you were to transform every ethnicity into a fantasy race in the setting, what'd it be?
Orcs. For all of them, except maybe Wildlings (they'd remain human).