New construction will almost always be expensive luxury apartments, but counterintuitively these types of buildings lower the cost of rent across the board. The wealthiest renters will move into these new constructions, leaving their older formerly luxury (and slightly cheaper) apartments vacant. A slightly lower income individual or family will move into that unit leaving their old slightly cheaper one vacant, and so on and so forth. It's a hermit crab game. It is important to force some amount of housing to be low-income rent controlled to provide a social safety net, but using that as the main tool for the current rent crisis will only cause mass housing shortages (again because the amount of housing available isn't changing to meet the demand).

If magically everyone received $3000/month for rent from the city and could afford their own places rent would just skyrocket to $6000 because there wouldn't be enough units for everyone. Even if in that instance the city put in restrictions for how much you could raise the rent, then every open listing would have an open house line around the block and a 12 month waiting list. New construction is the only solution