It's a weird assumption you seem to be making that businesses (especially small businesses paying minimum wage) are keeping more employees around as they actually need.
Maybe you've never worked for minimum wage. When I was pushing carts around at a grocery store, or delivering pizzas, and later leading shifts, labor costs are the number one concern at all times. If it gets slow and you don't need five drivers, you tell three of them to go home. Period.
They aren't (anywhere I've ever experienced) unnecessarily kept on the clock.
That's the reality of a minimum wage job. Increasing the minimum wage isn't going to free up the shift supervisors to be able to cut back further. They won't have a choice. So instead of a $2,000 nightly close for that pizza joint, it's going to be $1,800. And the franchisee pockets a bit less.
That's all that's going to happen. They'll still attempt to open up as many profitable franchises as they can. Close down the unprofitable ones just as aggressively, and still count every hour spent on labor.