Firing Grifol now sends a message that the White Sox are being serious
The Chicago White Sox are not a serious organization. Teams that try their best to win don't avoid spending on good free agents, they don't hire guys like Tony La Russa or Pedro Grifol, and they certainly don't allow their teams to reach 84 losses before the start of August.
If the White Sox ever want their fans to start taking them seriously again, they must start to turn things around quickly. It is going to take a long time for that to happen but they have to start somewhere.
That somewhere would be firing Pedro Grifol right in the middle of this horrific season. This season is unacceptable and multiple people need to go as a result.
Serious teams consider the future. Getting a different voice in there may show the players, fans, and everybody else that the White Sox are going to start worrying about the future.
Any player currently on the roster or prospects that come up would benefit from Grifol being gone. Serious teams do stuff like that.