If inflation was running hot persistently at like 6% then long term interest rates would be higher and housing prices would fall in nominal terms compared to wages.
The low-inflation, low-interest rate environment has produced high asset valuations due to the cheapness of borrowing money.
There is an important distinction on the spectrum between consumable things bought with wages and investments bought with borrowed money, and the rise in prices in those categories are different.
If you want to play the semantic game that all rises in any prices are inflation there is a real distinction that you're missing -- in which case we should talk about asset inflation vs. price inflation vs. wage inflation as being different inflations and stop talking about it like its the same thing (which economists would tell you it isn't by arguing that you're talking about assets and not inflation, but now we've just gone in a circle talking past each other because of definitions).