Of course there are huge problems with this -- what happens if whomever makes your food goes tits up, involuntarily (natural disasters, coups, ...) or voluntarily (maliciously attacking)? Who guarantees the system? How? Etc... --, if there weren't I wouldn't call it utopia. But I think raising the costs of war beyond the unreasonable is a net gain.
Note: I'm fully aware that this is an extremist and probably next to impossible position, no one has to remind me that. I just contest the fact that the objection "but then we could not go around and kill people" isn't a particularly good counter-argument for no trade barriers.
There are no tariffs on food, steel or similar between the member states. All states subsidise food production, but not steel.