Food is not an administrative cost because it is proportional to itself. By administrative cost, I mean that the more you have the more it cost you. Like for example:
1 city = 1 gold (1 / city)
2 city = 3 gold (1.5 / city)
3 city = 6 gold (2 / city)
4 city = 10 gold (2.5 / city)
5 city = 15 gold (3 / city)
The more cities you have, the more it cost per city.
Many board games create that sort of balance by limiting the number of actions a player have. So that when your empire is too large, it's much harder to manage since the number of actions per turn for a player is always the same. So limited actions has the effect of limiting empire expansion.