Haven't really seen any food api's. It would be cool if it did exist though.. But I don't think Just-Eat like services will bite since you'll be driving traffic away from their website..
But I see valid reasons for not providing APIs like that. Imagine someone creates a gadget like that and there's a bug, instead of 1 pizza it orders 10 of them. A delivery guy comes with 10, and no one is willing to pay for that many. It wouldn't take long to infuriate enough food joints.
Well, yeah, you could pay with credit card when placing an order... But I never do that, I just avoid using my card on web if I can easily do it :)