It's because the zombie infection resides in the brain and keeps the central nervous system from decaying. Once the brain compromised, the infection can no longer keep the CNS from decay, therefore the zombie loses mobility. Technically, I guess it's still a zombie. It just can't move anymore.
You could effectively "kill" a zombie by decapitation, but unless you also compromised the brain, the head would still be able to get you if you got too close.
You could incinerate the zombie, but that takes too long.
You could crush the zombie with a trash compactor or car crusher or 16 ton weight or grand piano or anvil. That would work.
The problem with zombies isn't that they're fast, or hard to kill, or even particularly deadly. It's that they are many and that they are relentless. You'll get tired eventually. Zombies won't.