The employees live in the city.
>Based off of complaints from the tech community, it also seems to be a city with a lot of homelessness
None of that is caused by having Google in the area. This is a cultural and a government regulatory problem (municipal, and state and federal to lesser extent).
>The problem isn't that workers are living in the city, it's that they're not working there.
If you're an employee you spend money where you live, not where you work. It would be nice for San Fran if all engineers worked in San Fran as well, but you can't have everything. Plus it wouldn't be so nice for Mountain View, Cupertino, Sunnyvale, Palo Alto, etc. In fact, those municipalities have more to complain about since they can argue they are nothing more than commuter cities.
San Fran should count their blessings.