Reducing demand at the top prevents the demand for high-end from overflowing into mid and low end. This does little good if the majority of people moving to SF are middle class. (Which they probably are because bell curves) To make a real difference you have to also add massive quantities of mid and low end --quantities about an order of magnitude higher than SF is currently planning. (going by the 10x disparity between population growth and housing supply creation)
And here comes the hard part: it's hard to build middle end and affordable units when neighborhood associations block the building permit until the developer pays multi-million dollar bribes (sorry donations). http://techcrunch.com/2014/04/14/sf-housing/
It does plenty of good because there will be fewer mid and low-end units occupied by high-income individuals and thus more available to mid and low income residents. This only has an effect up to the point where high-income supply catches up with demand, but we are a long ways off from that point.
"Market-rate housing probably has contributed to gentrification in many cities in the past. But the data shows clearly that, in San Francisco in 2015, market-rate housing development is not accommodating upper-income movers who would otherwise be somehow shut out of the city's housing market. On the contrary, the overwhelming majority of wealthy new residents do not live in new housing, and conversely, the vast majority of new market rate construction creates housing opportunities for existing city residents. For this reason, we find no reason to believe that either a temporary moratorium, or an indefinite prohibition, of market rate housing will reduce the number of upper-income residents in the Mission, or slow the process of gentrification that the neighborhood has been experiencing."
If you can only build 10 houses, and make 10% commission... are you going to build a shack? or are you going to build mansion?
The houses that get built, if the gates were to open wide, would all start off on the high end... while that would start a downward pressure, it would still be a very long time before those who can afford $200k for a house see anything in their range built.
What happens is that 10 people move into those new places and 10 people move into their old one and the vacancy works it's way down the line. Eventually some guy down the bottom gets slightly cheaper rent or a better place.
Imagine that instead 100,000 high-end apartments were built in the Bay Area. None of them will have poor people move into them but instead places like (to quote elsewhere in the thread) "downtown PA (university Ave) its right around $2800-3000 for a 1 bedroom, for places with 20 year old appliances and no upgrades." might now be $1000/month cheaper and affordable by somebody on a lot lower income.
Telling people that within 10-15 years if you keep building several hundreds of thousands of houses eventually rents will be affordable is not a winning slogan :)
New housing would start off being expensive because all housing in SF is expensive. Not the other way around.
Maybe the root of this fallacy is that it assumes prices are constant. If you build something today and charge $5k/month for it, that's how it will somehow remain forever. But in reality prices are set by supply and demand, for both new and old housing.
This is a common mistake. In reality, all added supply brings down price levels across the board.