Yeah, no... lol
Enma's hasn't served its purpose no matter which angle you look at it from.
If Enma's purpose is Oden's goal, then it hasn't achieved that yet.
If Enma's purpose is to destroy Kaido as Kawamatsu suggests when talking about swords in general, then it hasn't achieved that either.
If Enma's purpose is Zoro's goal of slicing Kaido into pieces, unachieved too.
I've got no clue what "Hiyori and Tengu" thing you're talking about.
They never suggest that Enma's purpose in this arc is to give Kaido a cut.
They never even talk about Enma's purpose in this arc.
Again, it doesn't matter if Zoro has been through more battles with it.
Zoro doesn't need to recreate all of Oden's experiences with Enma for it to be black.
Enma ALREADY has that experience of battle, hence Zoro needs to do little with it for it to be forged black.