I agree BMR is a scam, but not because of its effect on wages. It is too small of a factor, but because it is not market-based and leads to quotas, lotteries, middlemen, bribes- all bad.

To offset crazy high demand and prices, the only option is to increase supply (build taller, denser apartments/condos) or limit demand (disallow foreign buyers who speculate or invest, increase property taxes for owners that rent out their houses)