The assumption that median priced homes and median incomes should line up in way that the median household income qualifies for the median priced home is flawed.
In Southern California the percentage of homeowners is historically between 50-60% and the price to median income at the bottom of the cycle exceeds the value I compute when I use median income and qualifying standards. Look at the charts in Rich’s primer.
Why is the ratio higher than what would be supported by median income at the bottom of the cycle ?
Remember that half the population makes more than the median income. The bottom 25% in income distribution are not likely home buyers (assuming lending standards are back in force) so the median income of home buyers will tend to be higher than the overall income median.
I prefer to use the approach that asianautica outlines when comparing rent to own. Comparing monthly carrying costs of mortgage to rent. When those are close to even for a broad category of people (not necessarily the median income) the bottom is near. This is what happened in the mid-late 90’s. The nice thing is that this is what a reasonable prospective home buyer would use to determine whether or not to purchase, and it inherently takes into account interest rates, inflation, etc.