As to the other part of you question, “how should a house be”,
well again it depends. Even small children should have things that they believe belong to them. That is how they learn the difference between mine and thine. Just the same, their property clearly really belongs their parents, who can confiscate it if choose.
As for older member of a household, it is their choice in this matter should be respected.
My brother and I had a spoken agreement that we could use or do whatever we wanted with each others property. And it wasn’t quid pro quo. I gave him permission to do what he wanted with my things because that is what I wanted to do and visa versa.
I cannot say whether that is how it should be.