ive been thinking about this a lot but the hogwarts houses arent chosen by the characteristics you have but the characteristics you value.
that’s why most children are in the house their parents are, because theyve been told and raised by their parents to value these characteristics. and thats also why you get people that get sorted in houses they dont share characteristics with. you get stuff like cowardly peter pettigrew in gryffindor, follower-like and dumb crabbe and goyle in slytherin, and the whole weasley family (who have different personalities) in gryffindor, etc.
in the books, you can see that despite being incredibly dumb, lockhart was in the ravenclaw house. ravenclaw values intelligence; and even though lockhart isnt intelligent we can see he values intelligence. he knows that being intelligent will get him a better life (like making him famous), so if he cant be intelligent himself he’ll fake it bc he knows the value of being smart.
even hermione mentions it at the end of the first book:
even though she is the smartest witch in her year, what she values the more is friendship and bravery, traits of the gryffindor house, where she was placed. you can see it in the way that wormtail admired james and sirius, two people who were brave.
and i think thats one of the reasons you can “ask” the hat to let you be in a specific house. harry could be an slytherin through and through (he shares many traits - he is smart, cunning, etc) but those are not the traits he values, and when he lets the hat know this is when he gets placed in gryffindor.
and you can see in all the books that courage, determination, nerve, chivalry are all traits that harry values in people.
sirius for example, in spite of being raised to value slytherin traits, he disliked his parents and their values even before hogwarts. he values selflessness, putting himself in a place of danger to protect his friends and not understanding how peter could be so selfish and tell the secret, and not the self preservation that slytherin values. therefore, he wasn’t put into that house despite being raised to value that.
you can put this logic to almost every character, if not all characters. draco malfoy, hagrid, remus lupin, any weasley, regulus black, luna lovegood, snape, etc
i think its really interesting, because it makes you share house with someone who you shares values with, so it makes it easier to be friends with i guess. also if you’re surrounded by people who you share beliefs with, and you’re expected to be those traits, it gives you the push to become the traits you value (take neville for example).