Softening rents? That’s because you have a limited resource of people willing and able to pay $3000 to $5000 for a single bedroom apartment. It doesn’t take much construction to saturate that market.
The problem there is that housing is so insanely difficult to build in a place like New York or San Francisco. There are far more people who can pay $1000 for 1 bedroom, or $3000 for 4 bedrooms (roommates, typically), and it would be insane to ignore that market. But abusive zoning laws and the capricious permit process ensure that that price of housing would be unprofitable. So the big developers and financiers wait until the market goes to insanity levels before making a little boom of construction.
We need to reform housing, allowing increased density and by-right permit approvals, and then the little guy has a chance to build affordable housing.