That would imply that all following days have the same requirements, which is not the case at all, neither in the short term nor in the long term.

It does not. "each day" means you reapply the mantra every day to the then current state of your life. "for all following days" is the mechanism which forces you to most broadly consider the future and not just one day (as is the issue with "live every day as if it was your last")

Then I will argue that it doesn’t constitute a prototype, and it remains very unclear what criteria to apply for the day.