What would Zoro gain by having Mihawk's eye? This isn't Naruto where you gain special powers each time you trade eyes.
And why would they need to promise that next time they meet, they'll fight? At the Barratie, Mihawk already told Zoro that they will one day fight for the title and Zoro should "surpass" both his sword and himself.
Furthermore, we already saw a photo of current Mihawk when the marine dude was addressing the current Warlords to the marines and Mihawk did not have a missing eye since both his eyes and that ripple design.
One of the best possible theories is that Zoro closes one eye just so he can control his "killing intent" much better since Pre-TS it was wild - kinda like Luffy's CotSK around then.