Let's take a step back now that I have more time to respond. There are 3 claims that have been made in this thread (not all by you) that I'd like to talk about:
1. "focusing solely on your own income is too short-sighted. As the price of everything is dictated by the collective market (ie other market participants who also have disposable income). If you don't acknowledge this, then there's potential for you to be priced out of markets even if your income is growing, but growing slower relative to everyone else."
2. Redistribution can always increase median income when the average income is higher and we should redistribute to increase utility for this reason.
3. Recessions can be good because they decrease wealth inequality.
On your point #1, my claim is that the fact that I am citing real income directly addresses this point - people's incomes are rising even when you account for markets getting more crowded and people bidding up the price of goods. You say: "no, it doesn't account for point #2", which I agree with - I wasn't intending on responding to that point.
On your point #2 - this is one one where I mostly (although not fully) agree with you. Obviously there is no disputing the point around mean and median in the short term: that's just basic math. The issue is that there is no such thing as a "lump sum" transfer in a vacuum. If we could immediately do a transfer like the one you are suggesting without a shift in behavior, we absolutely should do it. But transfers impact expectations.
It is telling that you have picked land in Manhattan as an example since the supply is fixed so the effects I'm discussing don't play in - but for most goods and services people enjoy, the supply is not fixed despite your assertions. The US economy doubles in real output roughly every ~35 years or so (this may be slowing, ofc).
If you do a lump sum transfer to increase median income = average income, you will lessen supply in the future, causing a decrease in real incomes (supply-push inflation, as well as just economic downturn). Which brings us to point #3:
>>...or structure policy such that supply increases?
> You could. But how does that refute anything I stated?
This is my response to point #3 which was the original point I was disagreeing with. In a recession where supply decreases, that makes everyone worse off - there are fewer goods for dollars to competing over, nominal income typically drops, etc. etc. There is no redistribution happening here - everyone is becoming poorer.
It even makes the point you are making worse - if the average income/wealth is dropping faster than the median income in a recession (which is the point the original commentator was making), then the upside from redistribution only lessens. ie. if the rich are materially worse off, there is less to redistribute from them to the poor.