Say 200 people in the expensive houses move to even more expensive houses. Now only 50 families/couples are in the the life circumstances (marriage, promotion, inheritance...) to move form $250k at $650k+.

How does this effect people in the $200k houses? On average for each new expensive house 0.25 affordable houses opened up. Furthermore, since the expensive houses are about three times more expensive, per million invested we only got 0.25/3=0.08 of the value of investing into cheap houses.

So, it does help*0.08, which in discussion gets rounded down to "does not help at all". Admittedly, the discussion suffers due to this. So my criticism would perhaps be more accurately stated as that your last sentence should be

Therefore the $800k luxury home has created a quarter of a new $200k home, which is a bad deal.

In short: Unless you have a housing supply that matches the demand and assume additional constraints on the demand curve you lose quite a bit due mismatch/discontinuity/ lack of liquidity. For that reason adding expensive housing is a very ineffective option to help the masses of people looking for affordable housing.