I'm not against a minimum wage increase, but the country is watching places like SF and Seattle to see how a higher minimum wage plays out. The big players can always recoup loses in other markets, but the small businesses are unable to compete. Small businesses close, people lose jobs, and the wage hike is declared a failure. To me, if you really want to support a living wage, then don't support experiments that are doomed to fail.
If it's unprofitable for Starbucks to continue operating in SF, why would they do so? Big businesses can recoup short-term losses, sure, but if a given market is going to be unprofitable for the foreseeable future, there's not much reason to keep operating in that market.
That said, companies like Starbucks may see this as an opportunity to reduce competition, by operating at a loss until the smaller businesses close, and then raising prices to make the market profitable again. But if they actually do that, once they raise prices, small businesses can start competing again.
If they are even close to breaking even, then it's probably worth it to stay open in the area for marketing value.
Or you can just look at news articles from the past. There is long history of people predicting dire employment impacts that never materialize.
Back in high school, there was a big old dirty cafe all the kids hung out at. It had room for maybe 200 people on busy nights, which was probably over what fire code allowed. The coffee was made by stoned hippies on rarely-cleaned equipment and was pretty bad. It was normal coffee shop prices. It was the place to be because they were open 24 hours and had open-mic nights, where angsty teens could play guitar in front of their friends.
Another place in that same state was super tiny (seating for about 10 people) and had a line out the door most mornings. Their coffee was good, as was their pastry. It wasn't cheap at all. The service was pretentious and rude, but mostly in a funny way. Being a regular there felt cool, and you'd chat with other customers in line.
There are places in Chicago that charge >$6 for a cup of pour-over. These are typically fantastic. They could charge $7 and likely lose very little business. People who go to these types of places aren't cross-shopping Starbucks.
I'd bet that a place charging $10 for a cappuccino in SF would do just fine assuming it had something else going for it as well. Build a business that is Instagram-worthy and charge whatever you like for your product, and you'll still get lines around the block if it's a good enough gimmick.
Anyway, there's extremely little hard evidence of minimum wage raises leading to higher unemployment. Studies generally show no effect. There's no shortage of dubious anecdotes from people with a political ax to grind, though.
Also, how many people transitioned from a job at a small business to a larger one? Unemployment could remain unchanged, but competition could drop drastically.
As I've said elsewhere, I'm in support of paying a living wage, but I don't think it can work on a city scale and these experiments only hurt the cause by producing bad data.
If that is the theory, total employment would stay the same.