In a city like San Francisco, relative to the status quo ante easier development is more likely to result in slower growth in home prices, not a reduction in home prices.

But that's not the reason most San Franciscans oppose development. The primary reasons are 1) they're convinced more development will raise prices, 2) they believe affordability must be mandated through price controls or subsidies (e.g. developers dedicating X% of units for below market prices), 3) they insist on bike shedding every development proposal to death, 4) they're convinced private development is inherently inequitable (only "luxury" housing is built).

Pretty much the only group of people in the city worried about housing stock increases reducing prices are developers trying to sell-off new units. But developers are repeat players, and they're generally not the ones lending support to development hurdles. Though, there is (was?) at least one long-time developer who specializes in building "affordable" housing--mostly at public expense, of course--who did aggressively lobby for development hurdles, but carefully crafted so he and only he could easily get around them.