But, second, any objection that places the blame on "greedy landlords" is a total nonstarter. Everybody is responding to their incentives. Landlords aren't greedier than anybody else. If widget makers could set higher prices, they would. They don't because they can't, not because they're "less greedy."
SF is the second-densest "large" city in the US. I haven't found specific numbers, but looking at zoning maps at least 50% of the residential space is zoned for single-family homes only, with the majority of the remainder explicitly zoned for low-density residences. A big chunk of the city is basically a suburb! The rest of the Bay Area, of course, is more like 90% single-family housing. This year Berkeley passed a resolution removing single-family zoning throughout the entire city so perhaps the tides are shifting, but even if zoning laws and politics change, it'll take decades for this to meaningfully affect the housing supply.
Seems like the blame for the housing crisis lies a lot more with landlords who'd rather kick out a tenant paying X for a new tenant able to pay out X*y - if you have more people moving in than moving out, and existing landlords can simply choose to serve the new, wealthier ones, you're going to have a problem. If you couldn't take advantage of the migration simply by choosing to rent to the higher-income and kick out your existing tenants, maybe the politically-connected multiple-property-owners would figure out a way to get more construction going. We used to have both rent control and more densification than we have today.