Well, I think in the context of the parent comment, separating out housing would risk overstating changes in its effect on purchasing power because increases to housing would already be captured by inflation (since we're talking about real median income, which is already inflation adjusted)

I agree that housing affordability is a major problem and that looking at it independently could help you quantify if housing specifically has become more unaffordable, but that's a different question then whether the median person's overall purchasing power has declined (considering all of housing, healthcare food etc)

Yes housing prices are captured by inflation, but since housing prices are so different from region to region and city to city, just looking at a country-wide average median income does not say much.

housing prices and health care are captured by the "real" part of "median real income". Inequality is not, but as long as everybody is getting richer, I'm less concerned about inequality.

Inequality is still important even if everybody is getting richer (I disagree that everybody is getting richer, but that's a different discussion). Because wealth and power concentrated in the hand of a few means that a few have outsized influence on politics and society, which is very much eroding the fundaments of how a democracy is supposed to work.

Furthermore, there are many studies showing that more wealth inequality results in more consumption in a society. Which is not good for many reasons.