I think the fact the generally everyone needs (wants, at least) a dwelling confuses the matter. It's easy to think that because everyone needs a home, the economy for homes/houses is everyone. But really, owning a home is like owning a Picasso. Yes, it is unaffordable to most people, especially in specific locations. That doesn't at all mean that the price of Picassos is facing an imminent, steep drop. Because the people who can afford Picassos can, well... still afford Picassos.
That logic seems to be readily accepted by most people--that the prices of masters artworks are set by a small subset of people and that only the financial picture for that subset matters when determining price, and the trend in prices. A huge, worldwide economic downturn might in fact affect pricing, as many of the uber-rich see significant declines in their wealth. Or perhaps all the off-shore banks just take the money they hold and disappear. Suddenly, the uber-rich have less money to spend on things to hang on the wall of their bathroom, and simultaneously, more of them may actually take some of the art down from the bathroom wall and sell in order to be able to afford the property taxes on their many homes and the slip fees for their yachts. So, supply up, demand down=prices down. In other words, the market is not immune to basic economic actions and causality. But that action has to be within the subset of buyers in that specific economy. A decrease in minimum wage or SNAP benefits will do fuck-all to the Picasso market because it doesn't touch the members of that economy.
And this is true of the real estate (especially SFH) market as well. One has to separate home prices and the home economy from the fact that everyone needs a place to dwell. Living in a home has surprisingly little to do with the price of buying a house, in part because we have renters and shared homes an nonSFH homes. So yes, everyone needs a home, but not everyone needs to buy a house.
Once that distinction is made, it's easy to then revert back to looking at the basics of the Picasso markets. Picassos are available to maybe .001% of the population, so that's the sub-economy that drives the prices of Picassos. SFH in tough markets are affordable to ~5-10% of the people in those areas. (For the sake of simplicity, I'm not considering people who change locations to buy, though of course it is a factor) So it is only the economic fate of that 5-10% that drives the prices. If that 10% start hurting, perhaps in the face of a major equities correction, then it would affect SFH prices. And it may cause more people to liquidate, affecting demand which would further affect prices. Would an increase in, say, income tax on tips (not TIPS!) affect the prices of SFH in NYC or SF? Only in the most trickle-up, minimal sort of ways, as servers spend less, which means car dealers sell a few fewer cars so their owners make a few thousand less. The affect would be minimal, because servers were never going to buy homes in SF anyway. That change doesn't affect the sub-economy of people who are home-buyers, so it doesn't affect the price of homes. What a server can afford for a dwelling may affect rent prices for modest homes, but not purchase prices for already-expensive houses.
Average income doesn't matter when the average person isn't the buyer. Picassos aren't affordable to the average person. True, but entirely meaningless when considering what might happen to the future price of Picassos. The average man can decorate his bathroom with posters from Ikea. And that bathroom is in a rental condo, not a purchased SFH.