Where do zombies violate conservation of energy? They do wear down eventually, and fresh brains are low entropy and also nutrient dense.
The dullards who fight them never think of putting them in a hamster wheel and generating perpetual electric power.
Besides, the zombie armies never seem to have any logistics to keep them supplied with brains, or any support logistics at all. There's a reason why predators never evolved armies.
(Ok, army ants are predators. But they evolved logistics!)