I'm not claiming that they do. I'm arguing the opposite: if you build only luxury, it doesn't help poor people much, because most people will try to get the cheapest, nicest housing they can find. Building luxury units helps only to the extent that building anything here helps -- and if we believe the OP, it doesn't help very much at all.
Basically, this: you lived in Bayview, so you know who lives there. Knocking down every existing low-density home in Bayview and replacing it with market-rate housing would displace a huge number of poor folks. It probably also helps lower aggregate rents for everyone in SF by $40 a month or whatever, but that's thin gruel to the people who were there before.
This is the fundamental dilemma facing all construction in San Francisco.
There's no guarantee that building luxury housing lowers prices, which is what you were implying. You have to take it on a case-by-case basis.
(I lived in Bayview for a bit, and I was hardly the only tech person I knew who lived there.)