I don’t now about running but I agree with the non-fighting part. If I postulate than Zombie are dumb creatures that slowly rotten, I want to avoid them as much as I can until they are too rotten to move. It doesn’t mean that I can build defense and even traps but I should not confronte them but I will let the zombie population almost rot out of existence, hoping the disease doesn’t pass from the rotting bodies to the environnement.
If they run but are not smarter, they will be more dangerous but not undefeatable. The biggest issue will still be the big crowd. Zombie fear is 80% fear of crowd. People in groups are highly dangerous.