Prices are high because we have an inflationary monetary policy around housing. Essentially all mortgages are nearly risk-free to the lender, and are essentially implicit federal obligations.
Structural inequality is dangerous. All it takes is a little insurrection and the "faith and credit" gets depleted.
Hopefully we improve the stage of things.
Per Wikipedia, New York city's land area is 790km^2. Tokyo's is 2187km^2. Tokyo Metro's population density is 6,224/km^2 (I picked the higher of the possible numbers for this). New York City's density is 10,431/km^2.
There's really no argument you can make that New York should be cheaper than Tokyo based on density alone. Tokyo's big secret is sprawl.
Further people commute to the city's center which is why they tend to have lower population density than parts of their surrounding area. Which is why https://en.m.wikipedia.org/wiki/Guttenberg,_New_Jersey has twice NYC's population density even with shorter buildings.
Leaving Tokyo for Kyoto by train I kept seeing apartment buildings and houses for the first 50km or so.
For comparison the US median home price is ~220k. But, the Median price in Fairfax VA which is 30 miles from DC is $510,000. Chantilly VA which is ~35 miles from DC is 400k.