In every state I have lived, school retirement and health plans were handled at the state level. Hoping districts isn't going to shield you from your state government. The school districts pay into state plans as directed by the state legislature. It's the state legislature that's on the hook for the unfunded liabilities, not the school districts. School districts only make the equivalent of social security payments.

And it's not like the employees aren't playing into the system the same way that private sector employees pay into Social Security. Many/most state employees are excluded from participating in Social Security--the States in their infinite wisdom decided long ago that they would rather roll their own rather than submit to the tyranny of federal control.