Wouldn’t most of the zombies be piles of goo, eaten by vermin, or turned to zomcicles in the wintertime by season 9? You wouldn’t have new zombies.
You're right.
I think we are supposed to assume that the zombies want to eat people, but don't have to eat anything to live because they are dead.
If they are locked up in a barn for years, they'll be there when you come back for them.
It doesn't jibe with the known laws of science (but then the whole "dead but undead" idea is problematic and is hard to reconcile with current scientific thinking).
People also probably wouldn't be driving around in cars years afterwards, because eventually the gasoline would go bad.