Thinking about this, I think the problem is, not every class can become a minionmancer (or maybe they could, see below). The sheer action economy of having multiple bodies would quickly make some classes irrelevant in many situations.
And it's not like this is a Necromancer only problem. Other kinds of magicians should be able to get in on this as well. Enchanters could have mindslaves or charmed thralls aplenty. Conjurers could be able to have long-term summoned allies. Illusionists can have legions of Simulacra.
Then again, maybe Animal Handling should let you train a pack of guard dogs or wolves? Allow you to befriend animal allies ala Tarzan or Grizzly Adams or Dar the Beastmaster?
Maybe Fighters, I don't know, should have a subclass where you are a leader of men, with a capable lieutenant and men-at-arms following you around?
All of these things sound reasonable in a real world scenario, right? But that would change the game, much as it changed Gygax's AD&D game when his players hired a horde of NPC's to send ahead of them into dungeons. The combat rules as they stand would strain under the weight of so many actions.
The CR system would certainly be unable to handle things- how do you build an encounter with 4 PC's, 4 zombies, one NPC warrior loyal to the Fighter, 6 wolves, a summoned Efreet, and a pair of charmed Duergar? Especially when many of these characters are "free", acquired by abilities, as opposed to monsters, where every combatant takes part of the encounter budget to justify? And do you reduce the xp earned by the party for having minions, even though zombies don't earn xp (and were created via the Necromancer's spells)?
How long will battles take? How quickly will the DM have to start murdering NPC allies wholesale to get their game back in line?
I don't think the Undead Army Necromancer is not designable. But I think the game itself would have to be redesigned to allow for it.