I don't understand why people keep saying SF "needs" more density. Why? I'm assuming because the cost of living is so high? That is primarily caused by the Ponzi scheme of renter rights that make it so anyone renting for more than a few years is hugely disincentivized to move because they will lose their cheap rent, since their rents can never be increased to meet the market. So people stay in their crappy old apartment rather than upgrading, which reduces the inventory and drives up prices for everyone else.

Secondly, you don't just build apartments and you're done - a density increase requires more services to handle those new people. That's supermarkets, restaurants, hospitals, police, etc. All of that needs to be built up as well and usually isn't considered. If you DON'T add any of that, all you have done is reduce the services available for everyone in that area. What's the advantage of this again?

Finally, comparing the density of SF to Manhattan is not remotely accurate. Manhattan is the highest density part of NYC. SF contains a number of huge parks, mountainous areas like Twin Peaks, deeply residential areas like St. Francis Wood, etc. If you compare the density of the Mission vs. Greenwich Village or something like that, I could see it being relevant, but SF vs Manhattan is apples to oranges.