Your points are valid, and are well within the framework of NVC, so I disagree that this is a failing point of NVC.
> But here is the rub - maybe they are right, not you?
That is actually to be expected, and the book is full of such examples. The point is to get the conversation going. If their response is "You complain about productivity? The meeting is a whole hour long and I'm usually needed for only about 10 minutes of it. I do not see the importance of me being on time when I'm losing most of the hour for your meeting" then we're now in negotiation territory. Maybe I should change the format of my meeting. Or always have his item first on the agenda so he can come on time and just leave. The fact that he gave me this answer is helpful.
> it starts with "I am right, and you need to adjust"
I'm too lazy to reread the article, but a key aspect of NVC is that a request is just a request. If you make a request that is denied and get upset about it, then you never made a request to begin with - it was a demand. There's no "You need to change" in it. One thing that I find articles like these don't stress enough is that body language, tone, etc needs to match. You could take my original NVC formulation and speak it in a hostile way, or in a very non-confrontational manner. Of course, since we are communicating using written communication, this aspect is lost and different readers will imagine it with different tones/body language - which may explain some of the polarization I've seen when NVC is discussed in the written form.
And again, I have no disagreement with starting with "let's find the underlying root cause of the problem together" - it's not as if that violates NVC. I could state that in a horrible way as well:
"You and I are going to sit down right now and come up with a solution to this!"
If I wanted to say what you said in a more NVC way, it would be:
"This morning you arrived ten minutes after the meeting start time. I was disappointed that we couldn't go through the whole agenda and thus lost productivity. Would you be willing to discuss ways we can make these meetings more effective?" (this could include alternative times, alternative formats, etc).
(This time I dropped the word "late" because although I view it as a "fact", others tend to attach judgement to it).