Its a very lazy way of filtering.
"It couldn't have been that important" is their logic.
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.
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.
The solution is pretty simple: just fire the manager.
But that's very different than when an engineer stays up all night investigating a very serious issue, writing it up completely, and offering multiple solutions in a wall of text that can't be brushed off in Slack. The engineer makes multiple attempts across multiple weeks and communication platforms to get their attention, and it's ignored. Not "we're busy but will get back to you when we can." Just completely ignored.
A high performer (and really anyone) should not have to resign themselves to office politics to workaround this kind of dysfunction. It's imperative to fire such managers so that you don't lose the trust of the people doing the work.