"scarcity" being supply, and "wealth" being supply of money which translates to demand for housing. "demand" is people's willingness to purchase something.
> Building enough to push 250k houses to 200k would cost more money than the entire GDP and poor people still couldn't make the down payment.
You have it exactly backwards. Like I say, you're too focused on the literal cost. 250k vs 200k is entirely based on supply and demand.
Lets say we want low income people to be able to afford 2 bedroom 1k sq/ft apartments. To achieve that we need to build more 3-5 bedroom 2k sq/ft places. The wealthy will want the nicer apartments which reduces demand for the 2 bedroom place and that's how they become affordable.