I can assure you those artillery shells will wreck havoc among zombies packed together.
Even if they are not killed, limbs will be flying all over the place. And a zombie with no arms or leggs will not be much of a threat to anyone but a turtle.
Sure, if there was literally millions of zombies coming out of new york i can see how it would be a problem with ammunition.
But long before everyone ran out there would be a tactical withdrawal covered by tanks and those 50 cal machineguns mounted on just about every military vehicle today.