Wouldn’t it make more sense if Mihawk was crushed by Roger?
In all likelihood, Roger was the WSSM of his age.
Mihawk held Roger in high regard. He went to his funeral and even said that becoming PK was harder than becoming WSSM.
Furthermore, Mihawk losing to Roger would explain why he had a rivalry with Shanks. Shanks was Roger’s protege. Buggy even said he thought Shanks would be Roger’s successor. After Roger died, I’m guessing Mihawk tried to beat Shanks because of his relationship with Roger.
However, once Shanks lost his arm, Mihawk lost interest because he knew Shanks would never rival Roger in strength.