I suspect if the loss of these delivery drivers had such an impact on this hypothetical special place, they would hire their own delivery drivers to compensate. Worst case, you have to a call a number or use a mobile-friendly website instead of using an app.

If their existence is predicated on the exploitation of gig workers they should go under. The general demand for food won't be impacted by that one bit. Either people will be willing to pay more for their fancy burger or demand will shift to other businesses that can afford to pay their people a living wage.

EDITED TO ADD: Something that isn't often mentioned in these discussions is that the existence of businesses predicated on exploiting labour is narrowing the space for businesses that would be willing and able to compensate their workers fairly. Delivery apps are pricing out sustainable business models if they are allowed to skirt labour regulations, just like the common practice of Amazon and other companies treating delivery drivers as independent contractors.