Diablo can do that because it's a video game and primarily played solo. The game can track the doings of a dozen minions without the player having to make them do something individually every six seconds.
As a counter-example: The Elder Scrolls Online has a necromancer class and has a very limited selection of "pets". There is blastbones, basically a skeleton-guided missile, skeletal minion, a short lived ranged attacking skeleton (akin to summon undead in D&D) and spirit mender, a ghost who follows you and heals/protects you for a while. None are permanent pets (and ESO does have two classes with permanent pets). The rest of their kit involves flaming skulls, grasping skeletal hands, and conjuring tombstones.
Its very possible to viable a necromancer who doesn't walk around with a permanent army.