Zombies are going to be spectacularly unconcerned with shrapnel which would be quickly-disabling or -lethal to a living human. you could blow their legs off, or a hole through their torso, and they'll KEEP COMING. They won't be frightened by a grenade attack like a human assault wave would be, either. Oh, sure, the odd bit of shrapnel transiting a zombie skull will put them down - how many of those will you see per grenade? All the others in the blast and frag radii will keep right on coming, whether at reduced or full speed.
If you've got ENOUGH Mk 19s, then sure. I think you'd need a lot of them, though.
M430 grenade is designed to put 20-30 fragments/m2 at a range of 3m from point of detonation. Given a brain cross section independent of angle of approximately 0.02m2, that means a 2m radius is sufficient to ensure at least one and likely 2 fragments will transit a zed brain (since they aren't wearing helmets), and 1m would mean 5-10 fragments, basically ensuring lower brain damage.
So each grenade will reliably take out all Zeds in a 1m radius. At 300rpm cyclic rate, that's a clearance of 10m of frontage per second of kills. The additional fragments not transiting brains can disrupt bones and muscle, slowing zeds over likely a 2m radius. This means a single mk19 can continuously keep at least a 10m frontage clear of continuous zed flow, effectively regardless of zed density.
Against zeds with an average z to z spacing of 1m, this is 20+ zed/second/mk19, or 1200 z/min (likely half that for sustained fire).
To achieve the same kill rate would require an M2 to be fired SUSTAINED at its max cyclic rate AND achieve 100% head hits.
Basically, against human wave attacks, it's a matter of efficiency given aiming requirements, firing rate, and area of effect, in this case, the mk19 is extremely effective, without even accounting for limb disruption and associated slowing of the wave. In terms of mass efficiency it is also effective, as it's an average of one pound of ordnance per zed even if they are dispursed at 1m crowd spacing. Compared to a 50cal, to be as efficient would require 3-4 rounds max per zed, or 30-50 for smaller calibers. Given that trying to achieve 20 zed/second kill rates with other weapons woud require more than the sustained firing rates of any other crew served weapon, the mk19 is mathematically the optimum weapon for his type of defense, in both zed kill rate and ammo mass efficiency.