Zombies/WMG

There are various types of Zombies
This is why the stories differ so much on creation, reproduction, and extermination. A necromantic-raised zombie is different from a virus-raised one is different from a construct-raised one from a pharmacological-raised zombie. Woe to the person who confuses a magic-modded undead super soldier for a stumbling victim of drug-induced stupor.
 * "Zombie" has probably devolved into a generic term for infectious non-vampiric corporeal undead. Thanks a lot Romero.

If the world is taken over by slow zombies, everyone will be fine. But if fast zombies take over, humanity is screwed.
Slow zombies - only a few people taken by surprise and idiots will get killed, because they move so slow. Fast zombies however - those are a bit harder to escape.
 * Of course, Fast zombies are suicidally overconfident, meaning that a whole bunch of Speedy Zedheads will just kill eachother or jump off a bridge or climb an electric fence/ rickety ladder or something. The slow ones are really persistent, since their muscles decay less from use, meaning they'll keep moving for a long, long time. Besides, slowness prompts suicidal overconfidence in zombie hunters, believing them to not be able to get their trademarked Death Grip on a Survivor.
 * If the world is taken over by slow zombies it will be screwed because it was taken over by slow zombies.

Even if every viable corpse was to suddenly reanimate, and they were fast, zombies won't be the end of the world.
When you see a zombie movie, the individual zombies are no threat; the problem comes from the outnumbering humans. It's a dozen humans against billions of zombies with society in ruins. So if it is billions of zombies against billions of humans with working infrastructure (including well-trained armies), then things start looking less hopeless. And if they are scientific zombies that start with only one...