Then there's the fact that raising prices will still lose fast food places customers: For every person not buying it because it doesn't fit their budget, there's someone who just barely fits it into their budget that will stop buying it when prices rise.
This isn't theoretical: Companies analyze the price elasticity of their customers and understand roughly how raising prices X% will lose them Y% customers, and the amount of revenue Y customers represent, and whether that is higher or lower than the revenue generated by X. I don't work in the food industry or retail, but I have run that analysis myself in my own field.
I'm all for a living wage, but simply paying low paid workers more & raising prices to cover it is by no means a complete solution. Raising minimum wages is a bandaid solution. (And I'm not saying we shouldn't do that-- only that it's short term, and we need more comprehensive answers)