I wouldn't worry about zombies. They violate conservation of energy laws, for one.
Now I'm even more worried! How can the do that?
I.e. zombies are magical creatures, even less plausible than godzilla.
I also curmudgeonly think that Game of Thrones lost its appeal when it stopped being about political intrigue and became yet another silly magical zombie movie.
If it weren't for the zombies, the political story would just be about people fighting each other for advantage. The zombies add a tension between that and a common cause, since the threat faces them all; much like the world we live in today.
Even Lord of the Rings just had to bring in a zombie army at the end, but fortunately didn't spend much screen time on it.
The only one I like was the Jason and the Argonauts one where the hero fights a group of skeletons. The herky-jerky Harry Harrison animation is a pleasure to watch. And it was original.
(As for GoT, how many movies have had dragons?)
So the very first scene of both the books and tv show?
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!)