what the heck do you mean
One thing has nothing to do with the other. Zoros dream is wss the only way he can achieve wss is through beating mihawk which oda set up right in front of LUFFY his captain. Zoro unlocks adv coc and thinks of his promise to luffy which mihawk confirmed in his intro he would specifically wait for zoro at the top. In order for zoro to achieve his goal he has to beat mihawk.
As for
Mihawk is now Zoro's teacher/master. Would be a disgrace/dishonor for him to even challenge him again. What does this matter besides your own personal headcannon we just left wano in which we got zoro moment reaffirming what zoro needs to do for luffy that is become wss on top of that in egg head we got this panel...
Now sure if mihawk was as human logic as u claim him to be then maybe they don't fight lol but in verse zoro is hyping mihawk to be less humane then even his seraphim counterpart.
Finally, sure we do not know if this was self-inflicted or not but zoro left mihawk missing a eye. If mihawk did this, then that's enough in itself as proof that mihawk still means business.