It's not so much about today, tomorrow, yesterday or even days of the week. The bigger problem is perhaps with calendar days?

At least if you want your day boundary line up with midnight on the clock.

It would be hilarious to have everyone run on UTC, but have the calendar tick over whenever it's local midnight.

You ever run backups every Sunday at 2am UTC? Does that ever confuse you or the computer doing it’s job? If not, the problem you describe doesn’t really exist.

Ever talk to anyone who works shift work? Sleeps all day, works all night for a few days then has a few days off when they switch to daytime wakefulness? What is their concept of today and tomorrow?