It'd be a very expensive mini-series, at least for a few of the episodes. The book has a lot of battle and "swarm" scenes in the accounts of the survivors. Realistically, you'd have to cut a lot and change things - I'd probably cut it down to four narratives.
Either way, I think panic would cause more deaths than zombies. If you've never lived through a natural disaster, take my word for it -- losing power makes you aware of how tenuous normalcy is. I've been through Florida hurricanes. Even when my power was down, I could drive to a restaurant with power for a hot meal. Biking is also an option. And I knew normal would be back in a week or two.
That's more or less what happened in World War Z
. One of the characters mentions at one point that the Great Panic, with tens of millions of internally displaced refugees and general chaos, probably killed more people than the zombies while it the Panic was on-going. Areas that generally kept their shit together - like Jesika Hendricks' neighborhood in Wisconsin - didn't seem too bad off (and that was 2-3 months into the Great Panic).
If you really wanted to make it more difficult to control, you'd have the spread of zombies riding on the coattails of a dangerous disease, like with the 2007 I Am Legend
movie. A contagious disease that makes a significant number of people sick and kills a few hundred million people outright (followed by them rising up from the dead a couple of days afterwards) would be a significant shock that could cause massive panic, leading to a "Great Panic" style scenario. You wouldn't even have to resort to the Romero rule zombies where everyone who dies comes back.
That does deal with the paranoia of anyone being able to reanimate and how that would affect society.
I think people would eventually settle into a new normality about it. People at risk of dying would be monitored closely by their families, you might see stuff like Neighborhood Morning Check-ins to see if anyone didn't wake up from last night, and people who just passed away would have someone come up and destroy the relevant parts of the brain with as little damage to the face or skull as possible (I'm thinking some type of pneumatic bolt gun that could punch a hole in the skull).
Any other diseases would be taken very
seriously, since an outbreak that kills a bunch of people could lead to new zombie swarms.