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.
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.