IMHO the insistence on below-market-rate quotas is counterproductive in terms of the actual housing market (though it's probably necessary in terms of political feasibility). The BMR housing is _already built_: there is plenty of old, un-renovated housing in cities like San Francisco that ought to rent for far less than it does, were it not for the fact that quality housing is in such short supply that high-level demand spills over.
Concrete example: does your SF apartment have poor insulation? Single-pane windows? Creaking floors which are not level? In continental Europe, _that_ would be your low/medium income housing. Instead it's full of tech people because they have nowhere else to go.