It all helps. Relieve the shortage in high-income housing, and maybe they'll stop bidding up the prices for (formerly) lower-income housing because they had to live somewhere.
While I don't doubt that is the case, I do think it's offset by the high-income housing people then buying a second or third property as investment (gotta be a landlord, or you just haven't made it, I guess). I wonder if there is real data on this?
This is exactly the problem! People aren't happy unless the housing being built is low income housing. Building materials aren't made out of class concious magic, a premium apartment might be higher quality but the same kinds of contractors can often be used. We can't spite the rich here, we need a solution that leverages the market. Build so much housing for the wealthy that the demand will be insufficient to sustain the supply and then let the builders move on to the middle before finally the lower class housing types. People want to see homeless and poor people being provided for, I get it. But people also want efficient spending and that means supplying the top first to incentivize the builders to move down chain.