(My players please keep out, spoilers ahead.)
I have similar ideas, really based on when I was running Age of Worms and it all went to pot. (The PCs failed utterly to stop a monstrosity in a huge arena filled with spectators. A wave of negative energy killed most of the bystanders - which in 3e turned them all to wights.)
Wights turn those they kill to zombies. I'm just saying. (In 3e they even turned them to new wights - which really makes for a plague.)
There's no reason, in D&D, to limit it to just zombies.
(Even though a desolate landscape filled with zombies mindlessly trying to go about their old chores without success, only leaving their tasks to attack the living when those are nearby, is very appealing.)
Wights are a good firestarter. Some more advanced wights may well turn their victims to wights still, not just to zombies.
In Age of Worms the main enemy are
Spawn of Kyuss*. Spawn of Kyuss have worms that eat living brains and create new worm-filled Spawn.
A very visceral plague.
And what happens when other, more powerful, undead get wind of this. Will not vampires be in on this and use it to get enclaves of loyal humans that they protect by controlling the zombies?
I can see Death Knights or necromancers wanting to take advantage of it and carve out kingdoms, or empires!, of their own.
In my campaign, set in Greyhawk, animuses** left over by the fall of Ivid the Undying and the Great Kingdom will try to use it and plot against each other. At least one animus siding with the living.
Conflicts between evil begins - and perhaps the PCs can use that.
Fanatical paladins fighting the zombie hordes with all means. Perhaps some villages have to be sacrificed for the greater good - in particular if that means not having to cooperate with the Death Knights/evil cultists/necromancers/vampires who actually are trying to limit the damage for their own sake.
And what happens when so many undead congregate? When a city falls to the hordes?
Does not rifts open to the Shadowfell/Ethereal plane/Negative energy plane?
And what is behind it all? Is it Kyuss, trying to become a god? Vecna? Orcus?
Or is it all a mistake, a wizard trying to get more power than she could manage, letting it all loose?
* There was a
thread here making 5e stats for the Spawn. I'll get my conversion, based on the AD&D version up some day soon.
** Uh, well, animi really, but I fear that may make it less easy to see what I mean.