I dont know if i would say "food should be free", but I do think it makes a lot of sense to have "food stamps" both widely available and generously supplied for all who need/want them. From what I understand, far as economics goes, there isn't too many government programs which are as beneficial.
There is no shortage of food on Earth anywhere. However there are corrupt governments that withhold food from their citizens.
Well, there's some truth in that, but also I think one thing to consider is that a significant percentage of the world's population lives in regions/climates that just aren't very agriculturally productive. I sometimes think migration would be more cost effective for reducing hunger, than other routes we are trying.