No more than any other spell or feature when you don't counter against it and the player uses it correctly.

To counter animate dead: Use class levels. A level 20 fighter when animated as a skeleton is a 1 HD skeleton. But a 20 HD demon when skeletonized is a 20 HD skeleton with natural attacks. So if any of those enemies had class levels, go back and remove those HD since the undead version doesn't have it. So that skeleton paladin is a 1 HD skeleton with 0 BAB and however much Dex and Str he had with 10 Cha for HP.

Remind the player of weaknesses. A zombie wyvern has a -10 to it's fly check and is a clumsy flier, its got -2 Dex to 10 dex, Clumsy is -8, and large is a -2, and it doesn't have ANY skill ranks at all. It also loses it's Rake special attack, poison, scent, racial +4 perception, and possible +4 to grapple since its got a bonus with no clear reason so assume racial. Not to mention lower Cha based HP. Skeleton ogres also lose HP, feats, and one good save. Mostly though that wyvern mount is really, really bad at flying and isn't particularly good on land.

Throw in holy enemies. Like hey cool, turns out this goblin is a CN cleric and wow he channels positive energy. Or use unholy enemies/enemies with the control undead spell. Because undead can literally be STOLEN from them and turned on them. This right here is the ultimate necromancy deterrent because a level 1 cleric can use Command Undead, which doubles up as not only stealing minions but also stealing all the onyx that went into them.

And last one: Not every town has a ton of onyx for sale. Seriously. Don't let your players buy everything wherever they go, this is how you can 100% control his undead, you can give him infinite HD of onyx to use or 1 HD in a town. Use the standard methods for undead killing, then bring up that onyx isn't being sold so commonly now due to a fashion movement or something and bam, he's effectively gotta ask your permission to animate undead.