That there is room for improvement does not prove that a particular method would cause the desired improvement.
There is considerable reason to believe almost all variability in school performance is due to factors unrelated to the actual school itself (predominantly, the socioeconomic background and environment of the students and degree of parental involvement), which explains why limited scale efforts which require active parental choice to engage always perform better than the baseline, but scaling those up to be the baseline usually fails to have the same results. Better schools are just the schools attended by the students that would do best whatever school they were in.
So, if you aren't directing the solution at the things outside of schools that drive school outcomes, I don't expect you are going to solve any problem with the schools.
The inflexibility of the current system is an issue, at least the ability to try different schools/home school options allows people to try everything until they find what works, more so they can find a school that works best for their child.
Just like remote learning, if I don't like K12, I can try another online school, same as I dump Netflix for Hulu. I'm not even geographically limited. If there is a teacher that specializes in teaching dyslexic students and I have a child that's dyslexic, I'm no longer limited that the teacher isn't in a school within 5-10 miles. The teacher can be in another state even technically as long as she's board certified in my state. There is also a geographic arbitrage advantage, if my school system doesn't pay teachers enough to live comfortably in my city, maybe the teachers can be hired where its cheaper to live. Or teach for NYC and live in rural NY state.
We can postulate how a top down approach might work but these students will still be suffering while we sort and continually monitor (we won't) the system.
Involving market forces and allowing parents to have say in where their children will be educated puts the power in the most effective hands for change.
There's so much room for improvement.