But it doesn't make sense to change the basket from having 7 portions of meat to having 3 portions of meat and 4 portions of tofu (example pulled out of my ass, but the principle is the same as what's being done). That's what people do because of inflation to reduce their spendings, it still means that the number reported has nothing to do with real inflation.

Real inflation/deflation is the variation of price of specific items over time. You could absolutely check inflation of housing by comparing the price of thousands of houses that respect some criterias over time without changing the criterias.