Because there is no time to catch up once service starts.
A calm service. Whatever isn't prepped is missing exactly when all the tickets come in at once. A list per station shows what is still open before the doors open.
The same standard for everyone. Temps, new cooks and the late shift all work from the same list. Nobody has to guess what “the usual” means.
Proof of your checks. Many kitchens log fridge temperatures and cleaning as part of their HACCP-based food safety plan. Doing it in the mise en place list keeps those notes in one place.
Not legal advice. Which checks apply to you is something to clarify with your local food safety authority.