There's no clear reason stated in the manga (figures, he only used it 3 times in the whole series afterall...)
But if I had to guess, its probably because it's a last resort attack that requires too much stamina to do (3 sword style + making physical illusion of 4 more arms and 2 more heads)
also another point I might add, if you notice all the times Zoro used Asura, he always did it on land, not in midair, this could imply it also takes a toll on his mobility as well (carrying 9 swords would be heavier than 3 right...?)
and during the fight with King, he was in midair, so I don't think he could have activated it then and there, and just went with a new flying slash attack instead (Dragon Damnation)
but tbh in reality its probably just Oda not wanting to reuse the same attack twice in the same arc, it wouldnt generate enough hype compared to a new attack.
Probably it probably just takes too much stamina or some excuse
Out of story
I imagine oda doesn't constantly draw him with multiple arms and heads while fighting
Like unlike luffy and sanji with their enies lobby incorporated into their normal fighting style asura would be alot more inconvenient to draw
Because those are the only three times, he's been pushed to his absolute limits.
He almost died against King multiple times because of how lethal & dangerous King is, and at the end of the fight he was down due to the medicine's side effects. But if we're being honest, King never pushed KoH Zoro to his absolute limits to warrant Ashura. The tone of the fight changed right there, all of King's abilities (his sword tricks, his speed, his durability, his magma dragons, his flight) were countered; his strongest attack, sword & limb were cut and he was K/O'd by Dragon Damnation.
I believe Asura uses Conqueror's Haki, so Zoro can only use it selectively, as, until his fight with King, he wasn't actively using CoC.
Just because he's capable of doing the attack, doesn't mean he can use it regularly. After using it against Kaido, he immediately collapsed. It's a very draining technique, IMO, that, so far, Zoro has only been able to use under the right, dire, conditions.
I imagine Zoro will be able to use it more often as he masters CoC.
Honestly, it’s cause it seems very situational. It’s a one time attack that can cut through most other attacks, but that’s all it is, it’s a straight forward attack on the ground.
Against King which is a speedier type opponent who spent a good amount of time in the air away from Zoro, it’s almost useless. Zoro didn’t have any opportunity to use it or worse, I’d he does use it and it fails to take him down or worse King dodges it, Zoro exhausts himself and will likely be incapable of continuing. As Zoro has never been able to use continuous ashura techniques and has typically looked exhausted after one attack.
So it’s not a technique thats not great in many situations. So Zoro only uses it in few situations. But in the situations it’s built for, it’s devastating.
Because Oda doesn't want to.
Zoro is the only character that finishes a fight without using his strongest moves and the King fight was no different. Where's The King of Hell 9 swords style Asura, The King of Hell 9 dragon style Asura?
Because he was at his limit and with a broken body.
The Kaku fight is the best display of what Asura can do and why Oda saved it for a Yonkou, Zoro and Kaku were evenly matched but with Asura Zoro jumped tiers and neg diffed Kaku's strongest attack, oneshotted him and just walked away, latter we see Jabra carrying an unconscious Kaku.