Is this a terrible idea?

I'm a new nurse, working in a busy LTC/SNF/rehab. I love the work. I love (most) of the residents. I love (most) of my peers, but the management really leaves something to be desired. Schedules are a nightmare, nurses are quitting left and right, and the DON and ADON don't seem to care. So I have this idea. . . I work in a non-union state. We, as nurses and aides, have very little to no leverage when it comes to negotiating with our managers at this facility. I know that everyone, (yes, everyone)who works under these specific managers is very upset every time schedules come out, to the point that it feels like blatant disrespect. Days off requests are flat-out ignored, etc. So here's my idea: for the staff (nurses/aides), create a totally anonymous survey and ask a few key questions about what they would like to change about scheduling. Have a drop box to put them in, then collect them and go to the facility administrator and propose a mediation meeting between staff and management. We all tend to get so angry and emotional that I really think a mediator, an objective person who could keep us all on track, would be essential. Is this a good way to initiate change? Like I said, I'm a new nurse. I haven't been at this facility for a year yet, I don't want to lose my job, but some predictability, some reasonable rhythm and flow to each month's schedule would make such a difference, not just for me, but for all of my peers too. I miss the days of CNA at the hospital, where we filled out our own schedules (for approval, of course) every month. Why is that such a taboo thing at other facilities? Help?