Still beside the point. The Yonko (which Mihawk is a part of now through Buggy) are all vying for One Piece.
You have Mihawk's role to play in the endgame at this point, and he is heavily tied to Shanks to begin with, who is tied to Blackbeard. Not to mention, Ryokugyuu has it out for the Red Hair Pirates, and Ryokugyuu works for Akainu, who has ties to Kuzan, who is under Blackbeard and Buggy is also tied to Shanks.
You can, very clearly, see that a giant war is coming over One Piece. However, there is a very clear line of separation between all of these factions, and the Revo's/WG, the latter of which do not need to be directly involved in that fight and just wait for everyone to take each other out.
And you also have the fact that Mihawk himself has called the road to PK harder to achieve than the road to WSS. It justifiably makes sense for Zoro to achieve his status before Luffy does