Food should really have an impact on sieges.
I'm playing an Ottoman game, and I was sieging Constantinople. They were holding out very, very effectively. But, I did starve them.
... Then nothing happened. The population of Constantinople starved. They lost like 10,000 pops before I finally got smart, and sieged enough unrelated land to get 100% war score and force a surrender on the empire as a whole.
Historically, the point of a siege was to starve out the defenders. At a certain point, there would be nothing they could do but to surrender. One of the siege ticks is even food shortage, but it has nothing to do with actual food!
I assume the devs are working on it, among other things. But this just struck me as very odd.