It's a common misnomer.

Inflation is good for assets once those assets have been valued using an inflation appropriate discount rate. Housing rate now is priced based on a 2% discount rate, not 7%.

After the asset is priced appropriately for the current discount rate, then inflation is good for valuations.

Median wages drive home prices in the long run. It's possible home prices can be sustained if we see median wage rapidly gain over the next few years. Gasoline going up and driving CPI inflation doesn't make housing more affordable. Only increase in incomes/buying power.

Example: the 10y treasury was recently at 1%. If you bought that as an inflation hedge you would have lost a lot of money. Once people realize inflation is here to stay, they won't accept lower rates of returns.

Now it yields 2%, and soon likely 3%. Holding cash is better than holding a treasury during the repricing phase. Same logic applies for other assets.

Real home prices were super low in the 70s relative to today. Also wage inflation was very strong. I believe wages doubled over the decade. That alone implies a 2x gain in prices ignoring changes in discount rates. Not the same at all.

When the Fed starts raising rates to try to counter inflation we'll see mortgage rates follow. If mortgage rates go up to, say, 7% (pretty close to the average mortgage rate over the last many decades) that's going to impact the monthly payment. If people are just barely able to afford a house at a certain price with 3% mortgage rates, they're not going to be able to afford it at 7% - it all comes down to monthly cash-flow. As fewer people can afford to buy at current prices with higher rates that limits demand at those prices and something has to give - either prices will fall to accommodate, or the market will just stagnate. Even so, a stagnant market can only last for so long before some sellers start lowering prices because they have to.

This is essentially what happened in the early 80s when we had mortgage rates in the upper teens. If you look at home price sales history during that era there were some quarters where average selling price went down 10% or more.

Prices will stay high as long as buyers are not paying out of pocket. Once they have to pay more out of pocket with rising mortgage rates, they will notice that they weren't able to afford it in the first place and people will need to get rid of what they can't afford to keep paying.

I don't know about the US but the next move in the UK is to deregulate lending criteria. Allowing more people to borrow 5-6x income with tiny deposits.

People have always over extended themselves here to buy property.