scheduling a meeting is telling somebody that you consider this to be a priority and therefore they should too
The current situation I have is that I have 5 people demanding that I have their stuff as a priority, and they will schedule meetings to tell me such.
If I'm in 5 hours of status update and demo meetings every day how much actual work is going to get completed?
Therefore, everyone starts demanding meetings from you, because they have nothing to gain by not doing so -- you wouldn't use the extra time to work on their projects, but on the projects of those who insisted on meetings.
If you have so many meetings that you can't get actual work done, that sucks for everyone, but again, they have nothing to gain by canceling their meeting, unless everyone else does the same thing. But the others won't do the same thing, because now you have time to work on some projects, and they prefer those to be their projects.
I realize that this looked to the people requesting my attention like deliberate stonewalling. That’s because it was. And it wasn’t cool. But, “This quarter I didn’t ship any software because I was too busy answering email,” would not have earned me a satisfactory performance review. And I certainly was not going to openly admit to anyone but my immediate manager that I was using persistence as a prioritization signal. I saw what happened to the poor schmuck who made that mistake.