If the desire is to separate public and private schools or to bring all public schools under an agency controlled by the state government, (which the legislature could), then at least be transparent about it.
As stated, the FHSAA is a volunteer organization created by the schools and is over a century old. The state constitution allows for home rule and lets local governments, cities, counties, and school districts, to enter into agreements with other public or private parties. That really is all the FHSAA is in reality. For the legislature to take over a private organization like the FHSAA, I see such as unconstitutional and also against conservative principles.