OP - anyone who is claiming it tracks inflation is paraphrasing poorly. What Robert Schiller said was house prices track wage growth (published in "Irrational Exuberance"). Look at all the regional market crashes, those areas can have positive inflation and negative house appreciation, simultaneously. T
To find high regional and per city appreciation you need to identify areas with significant wage growth. Seattle is a good example (Amazon), that's a tough house market and they have excellent wage growth among the programmers. When Amazon 2 gets built most people expect the nearby house market to go higher (terrible if you are a moderate wage earner who doesn't own a house already). How does inflation predict what we all suspect will happen, that Amazon 2 will generate house price increases? The opposite is also true, in any small town that has a single large employer, if they go belly up the housing market crashes.
Please note, in the CPI calculations 25% of inflation is based on house price, which is why a lot of people make the mistake; it appears linked because of the correlation. But I suspect you've wondered why house prices drop in some areas and rise faster in others, but the inflation proponents say it should be uniform.