I'm really not sure that's true. I don't know exactly how many were built, but Melbourne (Australia) added a lot of CBD apartments and the price continued to shoot up.
Those were overwhelmingly tiny/cheap/low-quality/investor-bought apartments, but the fact is they were still there.
That there are places where foreign buyers outnumber locals ten to one, or other govt interference happens, do not refute basics of economics. Australian cities are tiny compared to Asia or even LA, and certainly units built were not in the millions.
i.e. if your locality has additional issues, the solution is to fix them. Don't use them as excuses to build less housing for folks that need it.
Those were overwhelmingly tiny/cheap/low-quality/investor-bought apartments, but the fact is they were still there.