Mihawk has to die to Zoro and he will break Yoru, that's the only satisfied way to prove Zoro unquestionably superiority as the new WSS, maybe put it as Mihawk gravestone.
Why keep Mihawk alive after getting the defeat he wanted? Let him die with his pride held high , instead of living a non-sense peaceful life that Mihawk finds boring, or keepinf challenging Zoro again.