Why do Zombies eat plants in "Plants vs. Zombies"?

The Zombies aren't interested in the Plants, really. They want to eat your brains. You're planting the Plants in order to prevent the Zombies from getting in your house. The Zombies say as much in their many Notes they send you between levels, and when they mutter "Brainz...." every so often.

First of all, you don't have to be neither a vegetarian or a vegan to eat plants. Vegetarians are people who merely do not eat meat. Omnivores eat everything (well, a diversity of things).

In the universe of the game, the plants defend the precious brain of the person(s) in the house. The game's zombies show a basic intelligence (contrary to the classic Romero/Brooks Zombie). This leaves us with two possibilities.

First

The zombies don't actually eat the plants -- they just try to destroy them as they seem to block their path (this explanation would not work for the digger-zombie, though, but maybe the digger-zombies are vegetarians and want to help their carnivore friends get some brain, but that's a hell of a stretch).

Second

They are fine eating plants as long as they are supplied but they start eating brains when the plant supply runs low. This would mean they're true omnivores.

Actually, the reason why the zombies eat the plants is because the plants themselves have brains. As evidenced by that one time Zomboss threatens to eat the plant brains in PvZ 3. That would explain why the zombies target the sentient plants and not the boring ones. (trees, bushes, grass, ect.)