And yet, Mihawk never actually took his title, so I´m not sure how that´s relevant.
But it isn't some olympic title or job position that gets auto-updated
It is world wide recognition on different levels and some times title can be here-say as well. For example Kaido's Title brings the most questions as the very chapter Kaido was hyped as WSC, his losses were referenced.
Whitebeard himself questioned the idea of him being WSM and Mihawk's dialogue true distance measure implies Mihawk was doubting the idea of him being WSM.
Mihawk's title is the only one that has been emphasized again and again, he wasn't portrayed as Shanks' equal when they met, he was portrayed superior, he called him inferior and has been.
Shanks was portrayed equal to Whitebeard when they met and equal if not superior to Kaido.