High school abolished? Yes. The replacement should be a system of standard tests that test competencies. You take the high-school graduation test, you pass, you graduate. You know what material you'll need to learn, so you can study at your own pace. It doesn't matter what age you are, and doesn't matter what classes you took. You pass, you're out, you're ready to move on.
To force students of various abilities and interests and motivation to march in lockstep until they're 18 is borderline child abuse. In other essays, I've said it's close to a human rights violation. I also think it's psychologically unhealthy to concentrate people of similar ages like that — it creates horrific societal distortions. Basically, it becomes the blind-leading-the-blind and prolongs childhood.
People tend to start growing up when they have to interact not with only their own age group, but with varying age groups. Such as a job.
The author puts it this way:
A careful look at these issues yields startling conclusions: The social-emotional turmoil experienced by many young people in the United States is entirely a creation of modern culture. We produce such turmoil by infantilizing our young and isolating them from adults. Modern schooling and restrictions on youth labor are remnants of the Industrial Revolution that are no longer appropriate for today’s world; the exploitative factories are long gone, and we have the ability now to provide mass education on an individual basis.
Lower the working age to 14. Make education competency- and skills-based. Allow students to progress at their own pace. And stop babying kids. That's why they don't grow up.