Restaurant profits are controlled by landlords. The rent goes up just to the point where the business survives. Due to the natural shortage of space, this works perfectly for landlords and not very well for anyone else.

What the minimum wage does is create an unmoveable barrier that can't be negotiated away. Minimum wage lowers the maximum rent the landlord can charge without killings the tenant. The wages come out of the landlord's pocket, not the business's.