The scenario you lay out would be especially ineffective here where cities are not part of counties so every population center would have several vaccinating entities with varying levels of "shit togetherness" around every population center here.
I don't work in San Francisco. So despite being high on the list because of my employment, if I had to be a resident of the county where I was employed, I could conceivably be a liability at my work as they try to safely reopen if I couldn't get the vaccine simply because I didn't work there.
However, as you note, I am much more likely to get my shot in SF because it is both a city and county long before my work county.