If you want to learn trig or calculus, it's set at such a
pace in schools that it guarantees that only the absolutely
best students will learn it.
It was a little more work for the teachers, since the system admitted that kids were at a variety of levels, but it was roughly a normal distribution, where a whole classroom of kids were on normal pace, some were a little bit ahead or behind, and a few were way ahead or behind. It seems like adaptive learning software could make this even easier.
The problem with today's school system in America (and likely elsewhere throughout the industrialized world) is that it's very much aimed at teaching the wrong people the wrong things in the wrong way (and that's when teaching doesn't take a back seat to day-care). The main goal is for everyone to memorize as much of a broad swath of "material" as possible, it's very much a teaching-to-the-test least-effort system. It's not geared toward maximizing each individual student's learning. Nor is it geared toward teaching competency and fully mastering basic yet key skills. Nor is it geared toward teaching useful skills that are key building blocks in the workplace, as a member of society, and as a functioning citizen of a democratic republic.
The steps necessary to improve this situation are fairly straightforward. As a start, reduce class sizes and hire better teachers, which is possible without increasing per-student expenditures provided the bloat in non-teaching staff and unnecessary expenditures is cut back (per-student spending has more than doubled in the last 3 decades, adjusted for inflation, the money has not gone to improving education, it has been frittered away). End the farce of overstuffed curricula. There is a monomania about covering as much material as possible, so long as students can retain enough to pass a test, but students don't retain much of the material and when the fundamentals are neglected they miss out on that too. Take the basics back to basics, emphasize the fundamentals (reading, writing, mathematics, fundamental science), learning them, knowing them, mastering them. Continue to refresh and test students on those fundamentals throughout their entire K-12 educations. And provide enough funding to allow gifted students to work at a faster pace, either within existing classes or in classes of their own.
I could go on, but that's a good start. Unfortunately, the biggest impediments aren't knowing how to improve, it's all of the interests and bureaucracy protecting the status quo.
As a start, reduce class sizes...
This, in particular, is something that I've done a fair amount of research on. Although the jury is still out, the best conclusion I've been able to arrive at is that for most kids, class size isn't strongly correlated with achievement, at least not within a reasonable range. Class size only seems to make an appreciable difference for kids that are "at risk", i.e., those that don't get much academic support at home.
So I might be jumping on you for just one small aspect of your opinion, but from the part of it that I do know about, I have the impression that you're just jumping on board with conventional wisdom that hasn't had much testing.
You might be able to improve some things like this, but to deliver it as a factual answer is a disservice.