Which means every city should do this to reduce their homeless population. The "don't do it because homeless people will move from elsewhere to get this benefit

Which means every city should do this to reduce their homeless population. The "don't do it because homeless people will move from elsewhere to get this benefit" is a race to the bottom. Housing homeless people reduces overall homelessness. If we do it enough, everyone will be housed. Part of this is lowering housing prices, another part of this is housing people who can't house themselves (for various reasons).