If low-end wages double, you have to look at how low-end home prices did, not median home prices. Housing is a positional good.
> If wages and home prices move up in lockstep (which they haven’t)
These numbers are all inflation adjusted, and inflation calculation includes all of those costs:
https://twitter.com/jmhorp/status/1308799186301747200
https://www.bls.gov/cpi/tables/relative-importance/2019.txt
Even if housing costs have gone up more than overall inflation, other things have fallen, and OVERALL inflation rate is the best rough measure of "cost of living". Focusing just on home prices or healthcare is incomplete way of understanding purchasing power / cost of living. When we say that the median income has increased adjusted for inflation, it means that the real salary has increased even accounting for the increased prices of all of the stuff that needs to be bought.
And finally, re-iterating the point: these numbers don’t represent a single earner’s pay history. It doesn’t really make sense to compare a single individual’s fixed expense in the context of these distributions, because they represent different individuals at different snapshots in time. While the shape of the distribution may be (moderately) fixed, the composition of it changes dramatically.
So yes, the point about inequality damn well is relevant. Anyone who wants to pretend they know about statistics should know that distributions matter as much as averages and medians.