To be clearer on my opinion on food sharing; I do think it should be allowable to an extent, but not in the form of a completely global bank. I think that you should be able to internally trade a limited amount of food, but that it shouldn't be open slather for completely adjusting the food in each of your cities.
Glad to hear you don't find the idea completely out to lunch!
I think its a fair point that there should be some restrictions on sharing food since it would otherwise be very easy (under the current population growth mechanic) to rapidly grow new cities by re-directing lots of food their way. That would be an overpowered mechanic and lead to contrived behaviours. Probably would be immersion breaking too.
I stand by the idea of having the capital act as a clearing house for food surpluses, however, for reasons such as:
1. Not inconsistent with history, where capitals were often the respositories of stores of grain (held against times of famine, e.g.);
2. Simplicity in execution - otherwise you'd need to manage many city to city transactions.
3. Dovetails well with other potential mechanics such as food upkeep for military units (could be done without linking units to individual cities).
As a compromise to your view, though, the ability of cities to draw on the empire "food bank" could, for example, be made contingent on having a trade route connecting to the capital and proportional to their distance from the capital. You could also limit food imports according to city size - smaller cities would not have the demand capacity, arguably, to import as much as larger cities. These kinds of calculations are not unfamiliar to the Civ series, having previously been used for upkeep costs, for example.