Are house prices inflation or appreciation? It may be unfounded but is an increase in value always inflation? (Serious question, not disagreeing with your statement.)
Modern days, the word "inflation" tend to refer to how government measures price increases based on a basket of core consumer goods. And in that case, appreciation and inflation are completely different things.
But when talking about housing/asset prices in aggregate, a 10% appreciation means you need 10% more money to buy the same asset, thus losing 10% purchasing power. Whether you call that appreciation or inflation doesn't make a difference.
Housing is a debt market. Houses don't cost 10% more just because prices have increased 10%. Manipulatedd interest rates have made debt service 15% cheaper. It's not that simple. Sure, you need 10% more for the down payment - I'll give you that.
The other specific thing about mortgages and other debt is that banks are a source of new money when they create loans. Banks do not even have to have a fractional reserve on hand any more, and have far more flexibility to create money as long as they can survive the stress tests. Which means that banks are far more in charge of the money supply than most acknowledge.
Which can cause a huge amount of inflation in housing, if there's not enough of it to go around for extended periods of time.
But when talking about housing/asset prices in aggregate, a 10% appreciation means you need 10% more money to buy the same asset, thus losing 10% purchasing power. Whether you call that appreciation or inflation doesn't make a difference.