Increasing the supply of the high end market often occurs while simultaneously reducing the supply of the low end market. This happens when landlords renovate their buildings. So it's very possible that adding supply can limit price inflation on the high end, while increasing costs on the low end.
Yes that’s gentrification of a neighborhood. Neighborhoods evolve over time. Displacement is bad but measures to fight it can be even worse. If no new construction can be approved over it being a gentrification signal, rents will zoom up even more. In the most competitive metro areas there are no cheap rent areas left within an hour commute.