That's one way to possibly solve the problem. If you've got a long time to work with and aren't concerned with what happens to the kids currently in the programs. It'd turn out badly in areas of low affluence. When California tried reducing class sizes without thinking about making more qualified teachers, as jobs opened at the schools in affluent areas, the good teachers ran to them and the schools in poor areas had to hire crap teachers just to fill the jobs. Quality of education plummeted right in lock step with how wealthy the neighborhoods were.
The other way would be to do what the top education graded countries do. All education free from kindergarten to college. Longer school days but about 50% of it extracurricular and fun. Highly trained and certified teachers. Low student to teacher ratios. Minimal standardized testing since the teachers are trusted to handle education issues in the class room and the low ratios and rigorous teacher certification actually allow that to happen. We happen to be doing the exact opposite.
I have a son in public elementary school and have dealt with the issues. The principal is a bureaucrat and low grade politician, but she isn't very good at it. She'd last about a month as a first line manager in a fortune 500 company. The superintendent is a pure politician. Neither has an education bone in their body. The teachers are all unionized, and right now they're forcing out one of the best teachers in the school because they keep expanding class sizes (past 30 to one teacher) and she's got the least tenure. Half the teachers suck so badly I'm surprised the kids learn anything. Some are decent, but badly undertrained or inexperienced and the huge class load burns them out.
There's a big push to use technology as a teaching replacement. Only problem is that many of the younger kids have no computer experience. What's worse is I live in an extremely affluent area, yet mommy doesn't want little Jimmy playing with her computer and many of them won't cough up the $200 for a dedicated machine for the kid.
This is the top end experience for public schools, due to the affluence in my area. Schools in run down areas are horrific by comparison. Private schools aren't much of a panacea. There is very little to go on when trying to figure out which private schools are good and which aren't. Many of the better private schools are religion based and after my experience with private Catholic schools, I'll just say no thank you. A lot of the private schools are really no better than the public schools and if you complain, they'll show you the door and keep your tuition. Plenty more people in line waiting to pay.
We know how to do it. There are dozens of countries that spend a fraction of what we spend and they don't depend on competition. Our universities and major companies are full of their graduates. We'll just keep doing the same wrong things over and over again (and moreso!) and hope to magically end up with a different result.