Well as a player you can(and should) pause and do the same thing. You don't even need to pause, really. Just spam detach siege on an unfortified province and fan out your troops . AI's been taught to do this recently, because players did it. AI imitating player behaviour is a good thing.
Sure, you CAN do this. Should? Much more debateable. The vast chunk of warscore comes from forts, and generally you can easily 100% any opponent just sieging forts. The real issue is that the AI can very easily punish you for splitting into 1k stacks to carpetseige; meanwhile, the AI is automatically bale to detect when your stacks are moving to destroy their carpeters and will generally consolidate back into a whole stack before you can arrive to punish their move. Meanwhile, the player must CONSTANTLY spam pause/unpause to avoid the AI punishing this greedy move (and it will).
For this reason I very rarely do these kind of strats in a war; maybe at the beginning of the game in a hard start where you need to micro your wars, but when you're finishing up a Great Khan achievement run and you control Russia + Persia + India + most of China? Nah, I'm not bothering with that. If you have the devotion to micro that hard all game, I commend you, but I think you would be in a very firm minority there.
I'm not arguing the AI shouldn't do it; I suppose when a 3k development monster attacks you as a 300 dev nation, your only real option is to carpetseige and try to annoy the player into going away. And thats my whole point, the carpeting is very very seldom actually effective, it just makes combat much more tedious and micro intensive in the late game. When you have 3k development it doesn't matter if the AI carpetseiges Russia; it's still not winning the war, and its extremely tedious to have to resiege all of that land when there isn't a easy macro button to do that. Detach siege works but is still tedious.
I'm not saying the AI shouldn't do it, I'm just saying that doesn't stop it from being bloody annoying and basically killing the late game for me. I actually couldn't bring myself to finish a Great Khan run that was nearing completion because i was getting soooooo tired of playing hide and seek with AI carpet siege armies in Central Asia, where they would just run as soon as your stack got close to them, and as soon as you dropped your attention to actually fight the important part of the war, they would promptly resplit and try to carpet again.