Oda may have not fleshed out the concept yet. He seems to have added the spirit/aura accompanying Zoro's attacks after his Mihawk fight. I'm not convinced the Mihawk fight was the impetus for their manifestation, there doesn't really seem to have been any indication of that.
So far most of these spirits provide mere aesthetic appeal, but they might further Zoro's demonic theme. Some of his attacks do seem to have supernatural qualities:
- Embina Yonezu Oni Giri: his swords wave and bend.
- (Kokujo Ou) Tatsumaki: he creates a tornado.
- Kiki: Kyutoryu Asura: he manifests two extra arms and two heads.
- Hiryu: Kaen: wounds inflicted catch fire.
The main reason to think there's something to the spirits is that Kaku implies that he created Asura with his spirit:
So perhaps the spirits that accompany Zoro have functions beyond mere aesthetics.
On another note, if like BOAT Asura is retconned to be an application of haki, I favour it being an advanced application of colour of armaments haki. Instead of welding your aura as an invisible armour, you shape it into solid objects (in Zoro's case the extra arms and heads). Others with these ability could e.g. manifest claws, gauntlets, real armour or other armaments with their aura. This is just a fanfic for now though.