Do you think a tedious amount of bookkeeping, even if the tedium is light, is a valid way to balance effects?
No. It doesn't balance spellcasting in any edition of D&D, including editions where they kind of expected you to track spell components.
Ammunition
quantity and availability can balance some weapons. Think of the more powerful weapons in run-and-gun FPS shooters. But the tedium of tracking ammunition? That just makes people want to play a
different game.
For example, if an effect could revive the dead, but only after at least 30 full moons has passed since the last usage otherwise it destroys itself, would this be a bad way of balancing this?
Seems not great to me. If the campaign is shorter than 30 full moons, then this is an unrestricted ability. A 5e D&D character can go from level 1 to level 20 in a few weeks of adventuring days.
But assuming that time scale problem is resolved, there also isn't a penalty for failure to track time correctly, or really any way for the DM to verify that the timekeeping is correct except to
also do the tedious task. Counterintuitively, the player is rewarded for
not tracking this correctly. If they get it wrong and go over, then their ability lasts longer or the DM has to police it.
I would prefer an attrition model of sorts, because it's really easy to see that the player does it. It that can also encourage the controller to do something with the army or otherwise do something to maintain it. Say at the end of N days, the maximum HP of each undead creature is reduced by 1. A creature reduced to 0 hp turns to dust. An undead creature that feeds on an adequate amount of whatever it's preferred form of food is returned to maximum health, but begins deteriorating again. Other forms of healing might work, too, or staying in a crypt or out of direct sunlight might prevent deterioration.
That does still seem like a lot of bookkeeping, though, so I would just recalculate the total whenever more undead are added. If you've got 100 zombies at 12 hp, and add 30 more zombies at 22 hp, you total up the hp pool and redistribute, rounding down. You'll end up with 14 hp each for 130 zombies. If the results make every zombie weaker, well...
don't do that. Power slips away in numerous ways, and an inadequate attempt to bolster it simply doesn't help. Attrition is gonna attrit.
Now you've got an army of zombies, and you either keep restocking it, give them lots of brain food, or store them in a crypt where they're not much use to anybody except small-time adventurers looking for a quick level.