"does anyone know where management is getting their insights to make changes?"
The latest Daniel Pink book. Remember the author interviewed during Diverge who admitted he couldn't manage his way out of a wet paper bag so became an author writing about management instead?
"Are there some surveys none of us are seeing?"
ROTFLMAO
"Do they care how many people think their management is being toxic or useless?"
No. Justification for their role was built on knowing all. They read the latest DP book. They can "layoff" anyone who speaks up and seeking input would make them irrelevant and reveal the truth.
"Do they care that there is so much overlap with roles and red tape in the processes that we can't get out of our own way to utilize them. Do they care that they are burning hours upon hours every week on disparate tools and processes?"
Possibly. Waiting for the new DP book on that subject to come out so someone new can become a VP claiming to know how to solve that while listening to absolutely no one on the front lines impacted by the problems..
"Do they think leadership from Public sector sales organization is going to breath new life into the org somehow?"
Desperation and no clue what else to do. Wonder boy flamed out after demolishing the once successful culture. Can't (probably) do worse.