This is the most sensible suggestion I've heard yet. At a stroke it removes the bitter conflict between LEAs and parents by ending the conflict of interest, levels the playing field for parents who cannot afford private reports, and eliminates the funding crisis for councils by centralising funding. I am sure there would be other problems (e.g. what happens when central budget runs out) but it ends the most contentious ones.
https://www.theguardian.com/education/2025/jan/05/a-plan-for-better-special-needs-assessment