The food supply chain is already mostly automated. Food is not cheap because of the service economy. It's cheap because it only requires work from a very small percent of the population to feed everyone else.
Yup. And some foods are unbelievably automated. There are GPS-guided, self-driving combine harvesters that will harvest an entire field of grain with essentially zero input of labor. Higher labor costs might somewhat increase the cost of some of the more labor-intensive crops, but your basic staples will still be cheap. If anything it's the cost of truck drivers that might have the biggest effect.