"The real issue is simply N > M, where N is the number of bedrooms needed in San Francisco, and M is the number of bedrooms in existence in San Francisco. As long as N > M, then there will be winners and losers."No. This is a toy economic model that doesn't account for time or land constraints.
The benefits of construction do not immediately and equally accrue to all market participants. In cities where essentially all new construction is infill (i.e. San Francisco), new units will displace older, cheaper units (not always, but it does happen). Therefore, until supply actually exceeds demand, you will have winners and losers, and you must account for the losers.
Additionally, an any realistic model of housing, you will see that new construction will continue not until housing is as affordable as existing stock, but only until it is no longer profitable to build. It is expensive to do infill development, and therefore unlikely that any builder will continue to generate supply until prices match those of older properties. It could easily take decades for new construction to lower housing prices. For example, New York, Paris and Tokyo are far more dense than San Francisco, with more liberal development rules, yet are the some of the most expensive cities in the world in which to live.
It is thin gruel to say "I'm sorry you lost your currently affordable housing, but come back in 20 years, and everything will be affordable!" But this is essentially the response you are making.