Introduction of the Sorting Hat
I think it would be to implement the sorting hat or some kind of mechanism so that you know which house you belong to for players who have doubts and that it can be used regardless of the player's level, that is, it could be used at any time of the game . This does not mean that the free choice of any house is bad, the two options can live together.
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Comments
It would be cool to have test of sorts of questions of ethics, interests, proclivities & situational answers that does not lead a wizard to know how to answer but does have a hidden meaning & then sorts you into a house without the choice of the witch or wizard. There are way too many Gryfindor & Slythrins by choice. I suspect some of them would be Ravenclaw & Hufflepuff statistically.