When people in NYC are driven out of their neighborhoods because of gentrification, they generally move down south. There isn’t some magical part of town that they can afford with their “current budget”
Economic theory says some things are theoretically impossible, no literally, but economic theory wouldn't say that here:
The local housing market is much more complex than supply and demand, with larger economic factors (e.g., interest rates), very imperfect information (affecting everyone from buyers, to sellers, real estate agents, lenders, etc.), coordination by landlords (e.g., RealPage), non-economic factors such as prejudice (or just a co-op board!), government actions, larger trends, temporary inefficiencies, etc.
Economic theory is useful, but it does not predict or circumscribe the immediate reality of individuals. Life is much more complicated than that.
First, I didn't say there is no supply effect; I said it's far from impossible for the effect to make a difference.
Second, many factors are involved in a complex market; you and I don't know how much effect the supply had in this case. That you are interested in that input isn't evidence of its effect.