Although I would like to see wine added as a food source, like beer, I'm not sure if I want oil to be added as a food source, I know you would cook with it, but it's kinda like salt, you cook with it in very very small amounts, but don't eat it to fill yourself up.
I've never had an issue with food but my parties always need food to help them(in army), I keep getting points for giving my fellow troops in my army food. So I wonder if food isn't an issue, but the amount of food your other parties carry?
As for cities starving, seems there is a population issue, like your farms have a max production and will never increase, wile your cities can just over populate and keep asking for more food.