The effect of not ever getting into the workforce at all is devastating to those few that don't make the cut. Meanwhile, the effect of a couple of dollars extra to those already in the workforce is comparably small.
Consider that minimum wage could be raised arbitrarily. If 10$ is too low and 15$ is better why isn't 20$ even better? Why not 30$? The argument for which cutoff to choose can't be based on some basket on what people need to live a certain standard (i.e. a one-bedroom apartment in some urban area).
> Do you really think Subway franchises are running on such razor thin margins that they'd be forced to shutter stores if they had to pay their workforce marginally more?
Some of them certainly do. Subway is in decline:
https://www.businessinsider.de/subway-closes-over-900-us-loc...
Lots of low to minimum wage employers indeed do have razor thin margins. For example, Wal-Mart only has about 4000$ of profit per employee. Companies like Amazon only lose money on their fulfillment centers.