I think you are bringing "parents" into this unnecessarily. If there were Gryffindor noble chambers, I doubt anyone would deny one to Harry on the grounds that he was an orphan.

He's still inheriting their status. The fact that they're dead is immaterial.

Conversely, if a hypothetical Malfoy of lesser parentage (a cousin X removed, perhaps) were to enter Hogwarts, I doubt they would be denied noble chambers because their parents were low down within the Malfoy hierarchy.

Being a Malfoy is apparently higher status than being a commoner.

It's not about inheriting parents' status, it's about membership of a noble house. Membership of a noble house confers the right to noble chambers where they exist. It confers a bunch of legal rights, as we saw with the Wizengamot, which again are not restricted to adults. It apparently also confers the right to speak on behalf of the house.

One of these things is not like the others. Being a US citizen also confers a lot of rights. That doesn't mean you have the right to negotiate treaties on behalf of the US.