If food aid weren't given, the population would die off until the balance point of food available compared to population and infrastructure.
You're wrong about this for the most part. The people would relocate, and that's really what food aid is about: keeping them from migrating.
Moreover, food isn't a valid concern in overpopulation. We have plenty of food. We even have the resources and infrastructure to transport that food. Economic costs can be ignored in the case of aid work. The real problem, imo, is the fuel we burn to produce and facilitate the abundance we enjoy. As developing nations mature, this problem gets much, much worse.
People seem to think that climate change is a technological problem. It isn't. It's a population problem. We could be burning fresh timber for our energy and we'd have the same issue. Climate change might have a technological solution, but then again it might not. At least not in time-- especially not in developing nations.
Once you get people thinking along these lines (which is not easy based on how many downvotes I've gotten and upvotes opponents of my opinions have gotten) you still have to struggle with the idea of restricting population growth.
Whose population do you restrict? Why? By how much? Do you kill people to meet your goals? Or do you just say "fuck future generations" and let the world warm? If cheap green technologies are developed and overpopulation stops being a concern, do you force those technologies upon the developing world? For free? Why or why not?
These are hard questions that deserve answers and we, as a global community, aren't even considering them.