If you replaced every low income unit in SF with twice as many market-rate apartments tomorrow, you would raise those individuals’ rent to some value near market rate.
Assume there are 100,000 rental units in SF and 50,000 of them are low-income units. If overnight you replaced those with 100,000 units that will float to market rates, you are correct that the displaced individuals would now have no units available that are significantly below market rate. However, the market rate will not be the same as what it was previously. It will go down based on a 50% increase in supply. From an economic standpoint, the same thing should happen regardless of what percentage of low-income housing is being replaced. Whether or not this goes down to the artificial price they have in low-income housing depends on how much more supply is being introduced into the market.
> there are hard floors on new construction rent.
If you are saying that the price set for "affordable" housing is so low that new construction couldn't even break even at that price, then there is a whole different set of problems involved in addition to supply and demand.