Yes, pay is lower in government service than in the private sector. But pay is not the be-all, end-all. As someone with management experience in the Nonprofit Sector, I was also in a similar position where I could not compete for hires on pay alone; it forces you to get creative.
Its not that we are unaware that problems exist. It's not that we don't want them solved. The problem, dear readers, is that no one wants to do the hard work required to figure out what is actually causing the problem.
Every position I have taken in my professional life has been in a crisis for the organization or the department. Each of these represent a major challenge, but I have also found that they present the best opportunity to have the greatest impact.