All that would happen is those other places would become dependent on the free food we send them, and certain of their domestic industries would be destroyed as they couldn't compete with the cost of free food being dumped into their economy.
Also here domestically excess food would no longer be produced as if you don't produce any excess you don't have to pay the cost of shipping it, or doing anything with it. Everything would become "just in time" or made immediately 1 to 1 with a specific request. So the post scarcity impression we have now would go away pretty fast.
So I don't think we actually are post scarcity with regards to almost anything currently. Efficiency is very high I would say, so high, and we're so productive that we occasionally end up with wasted resources caused by poorly estimating demand.
Unfortunately, before any of that happens, security, police, and military will be going post-scarcity, while those in power are pretty selfish.