To me, he'll eventually use it
However, the main question for me is, was Asura actually Haki related? or not... cause according to what we know about it, it's created by Zoro's spirit... spirit in One Piece is usually translated into Haki.... which will lead us to one of three conclusions on why Zoro didn't use it thus far:
1- Either Asura is actually a "Weaker version" of true mastery of Haki... and thus, because Zoro became able to utilize Haki BETTER, he doesn't actually use it in Asura form, rather in what we see....
2- OR it's another advanced shade/technique of armament haki (different from the one luffy learned)... just like Observation has different shades like hearing thoughts (Coby)/ feeling emotions (Luffy)/ reading moves which has Future sight as advanced form...etc.
So, in the same way, Armament Haki MIGHT have Different shades... and Zoro can use armament haki, casually, but Asura is an advanced shade he utilizes for it (different from the advanced techniques Luffy learned)
3- OR, it's not a haki related... it's just a different ability (maybe related to cursed swords or something else) and Zoro can enhance it with Haki...