There's also the argument that economic diversity is good for everyone. Non-market solutions to maintaining space for people of different income levels in the area might have positive externalities.
It almost seems pernicious to have low income housing since it allows employers to get away with lower wages to cover an artificially low cost of housing, at the same time, service workers retain a poor quality of life because outside housing everything else is expensive.
Your second point is interesting, but I suspect only partially correct. I imagine subsidizing service workers to live in low income housing does allow businesses to pay service workers less in those areas. However, if those low income housing units were not the service workers best option - they wouldn't live there. So I would imagine overall that it does help the service workers, not hurt them.
http://dailysignal.com/2014/06/10/drilling-innovation-forcin...