I think to some extent some of the pushback is the prompt folks not understanding that sometimes lateness isn’t something they can control (e.g., meeting with important set of stakeholders that you can’t duck out on early ran late)
And the late people need to understand that sometimes they will miss the beginnings of things, but that's ok too; their inability to be on time (for whatever reason) should not waste the time of those who get there on time.
So then you waste even more time when someone recaps for them.
It's almost like people need to think about their day when they're scheduling things instead of just accepting every single meeting.
You can request different times for things. That's an option.
But there are people where shit seems to happen more than for others. Late once in a blue moon? No worries. Repeat offender? That's a you problem.