Earlier quoted context omitted.
I'm not sure what you mean, but I'll try to express myself more clearly. In the most basic sense of economics for prices to fall supply has to increase more than demand. If demand increases more than supply the opposite is true. There's nothing saying that a more supply can't also increase demand or even increase demand more than supply. When more wealthy (or ambitious) people move into an area it often leads to that…
Yeah, this is one particular kind of gentrification cycle that's sometimes seen in cities (most clearly in parts of Manhattan). Higher-quality new housing is built, which is one part of making an area more attractive to more affluent residents, which drives up prices despite there being more total housing available than before. What of course is less agreed on is how to untangle all the interacting causal factors her…
If you don't construct luxury housing, it's not like you can keep people from moving in. Witness all the tech employees living in genuinely terrible Mission apartments. All that happens is you end up with gentrification that works around construction laws: old single-family homes being converted into hacker houses, run-down houses being rented by well-paid tech workers, with lower income people being forced to move ever further away.
Objectively, most San Francisco housing is really not attractive. Yet rents are still extremely high because there is demand despite the poor housing. It makes far more sense to construct efficient luxury housing which can soak up the luxury demand so high-income earners don't end up taking over the traditionally affordable housing.
Now that the construction pipeline is finally coming through, we're seeing this effect and rental prices are starting to fall. If your theory were true, we'd expect rents to be rising now that construction has finished—the exact opposite of what has happened.
It might be possible to make an area unattractive for gentrification, but I think it's pretty damn hard. Construction bans certainly don't do it. Not even violence does (though crime as an affordable housing strategy is significantly under-researched).