They Can't Heal from Day to Day Damage
One advantage to having a fully-functioning central nervous system is that it also does a damn good job of letting you know you've been damaged. It does this by way of pain. Think about all the paper cuts, stubbed toes and nut shots you have suffered in your life. Now imagine they never healed, just sat there and rotted while you continued to rack up other paper cuts, stubbed toes and nut shots. Pretty much every wound you've ever had would end with an amputation. One thing we know about zombies from Romero and Fulci is that they are a clumsy lot, walking into doors and helicopter blades without a second thought about what kind of damage they are suffering.
While complete insensitivity to pain seems like an awesome superpower in theory; in real life, you wind up being more like Mr. Burns than Wolverine. Congenital insensitivity to pain
is a neurological condition that some people are born with, meaning they don't feel pain. They can feel everything else, but the absence of pain means they accrue damage to their bodies but are unaware of it. Even with the ability to call for help, loved ones watching out for them and our coddling society, this can still lead to all kinds of terrible ****, like infected body parts and bitten off pieces of tongue
All the dings and bangs zombies will suffer after tripping, walking off of bridges and stumbling around on dark cloudy nights will eventually leave them limbless, toothless and with every bone in their body broken. Seriously, in the event of the Zombie Apocalypse, just stay inside, watch all the episodes of 24
back to back, then walk out on your lawn with your Corpse Rake and tidy up (you will have to buy a Corpse Rake, however, if for some reason you don't already have one).