I think education is actually case where the free market would solve a lot of issues. Making schools compete for students would incentivise schools to provide a more valuable education.

You end up pricing people out of the best possible education unless you regulate heavily, at which point you may as well have state-run education.

As opposed to state run education where the best possible education is available to everybody? Is that what we see in public education?

We do see this in Switzerland, Finland, etc. But this is due to a competent Department of Education, which simply doesn't exist in the UK. Infact the UK DoE isn't even just incompetent - it is quite clearly maliciously sabotaging education, there is no other logical conclusion for the farcical policies that are in use.

What kind of UK policies are you referring to?

Or you have state-run education as another competitor. Or you can have the state sponsor promising but poor students. You can even incentivise private enterprises to give bursaries to promising but poor students.

You could use a voucher system where everyone pays nothing although I don’t think that would be optimal.

Who wants the “bad” students? Bad could be from a behavioral or academic standpoint? Don’t they deserve a chance at an education as well?

As long as ‘bad’ students have a voucher, you could ensure that public schools take them.

You want to provide quality education to __ALL__ of the population. I don't mean university level education.

I mean real world education, such as how their body works, how to navigate society, critical thinking, cognitive biases, how probability works. If humanity is to survive we need to move away from empiricism and dogma, we need to move towards an educational system where kids grow into rational adults.

I agree, except for the move away from empiricism part, empiricism can be quite quite useful.

Cynical take: they don't want an overeducated population as that poses a mortal threat to the system.

Could you elaborate? There are at least 2 interpretations of “over-educated” people being a threat to “the system”.

Overeducated as in having university degrees and being “highly skilled” which demands imports of “unskilled” workers which causes integration problems.

Or overeducated as in understanding how “the system” works and are aware of the class war they were thrown in since their conception, how the system pits the working class against each other while the ruling class enjoys a paradise.

The second interpretation of my comment is what I was attempting to allude to. I am reminded of this particular quote from Orwell's 1984: "Until they become conscious they will never rebel, and until after they have rebelled they cannot become conscious."

Sounds like Orwell was paraphrasing Plato. Funny, effectively the same issues 2500 years later...