Actually, the true threat of zombies would be the whole horde aspect. They don't need to move fast, be particularly strong, whatever. There used to be a great browser based game called Urban Dead which brought this to head. You could be a survivor or zombie. Survivors could speak and relay plans to each other, barricade buildings, manipulate machinery like guns or generators, whatever. By all means, they should have had the upper hand and usually did.
That was until the number of zombie players outnumbered the survivors. See, the zombies communicated with groans that traveled a certain number of grid tiles. If you, as a zombie, heard tons of feeding calls emanating from one location, you ambled on over and began clawing down defenses. 100 turns to 200, 200 to 400, soon there'd be so many zombies so as to crumple down any defense.
There also the human aspect. Sure there were survivor militias and people role playing as drunk celebrators in emptier parts of map, but then you'd have people playing cultists who would tear down the barricades from the inside, serial killers who would stalk and murder people who were alone, people who would drop in and kill you if you held a place of strategic resource. The game was chaos and a great representation of how shit would probably go down, because it was all real people just role playing whatever they wanted within the guidelines of the actual game.
