That is not how reality works. Prices go up because people are paying them - it has nothing to do with government. A seller wants the highest price, no matter what the govt or local markets do, and a buyer wants the lowest price, no matter what govt or local markets do. Each is competing against other sellers and buyers. At no point is the govt telling a seller they're too low or a buyer they're not high enough. If either side dislikes the deal, they walk.
It has nothing to do with being an asset class - the causality is the other way. Houses are valuable, are a significant amount of money for most people, and increase in value because, if nothing else, inflation - thus they're an asset. So is holding cash (which actually deflates in value, yet is an asset), so are bonds, stocks, annuities, pensions, and on and on.
As to the shoe example - here's more what happens:
People would all love it for their cars to increase in value, but in reality they do not. The govt is not making this market out of magic to satisfy people's desires - houses increase in value at slightly above inflation because the market values them so.
By your reasoning, govt is magically making prices go up, but the market would not simply follow along.
And, if the govt were magically making prices go up against market wishes, they're doing a terrible job at it - housing only increases around what other assets do - and that's the market doing it.
People have tried using govt or other forces to misprice markets, but that never lasts very long before wise investors pull the rug out and crash it.
History has a lot of examples of people both trying to fake high prices for force low prices by law and losing out to the market. The market commands vastly more resources than any govt to put things in check.
