The most advanced and best classes I had were small, Socratic, and had take home tests. We were able to get through a lot of material, in a lot of depth, because people did the reading, but a big reason people did the reading is everyone liked the class and the professor (granted, this was college).
When I ended up teaching during my PhD I mimicked his style as best I could. Made my course very project based, made homeworks easy to get good grades but also included ways every student could expand on and gave lots of feedback. I like to think the students really liked me, as they would frequently stop by my office just to say hi and a bunch would show up the next term either showing me how they expanded their project or wanting to talk about how to do more or just general advice. YET only half the kids ever attended lecture, a third of kids chose to do a final project not much more complicated than homework, a few didn't turn in their final project, and 2 grad students complained to the department when I failed them for not turning in their final (they ended up being given Cs). This wasn't long ago, early GPT and tail/just post covid days.
There's just a time problem with doing the grading in class. You cannot cover as much material. An ideal class is students do reading before lecture, you go through the material together and have a healthy dialogue about where there is confusion, and then the students build on the solid foundation you created. This certainly works for high school and college, though I suspect not as well for lower levels due to lower independence. The unfortunate truth is that when teaching you're also teaching students a lot of auxiliary skills too, like time management and self-reliance. If you aren't teaching students these skills, where do you think they are going to get them? Sure, some will be able to learn them themselves, but you can't look at their success and claim victory through survivor bias.
But I don't think this is the whole problem.
I'll be honest. My experience with students, the big reason for them cheating is grades. Covid and GPT exacerbated the problems[0] (and created some new ones), but a lot stems from what was already there. We place so much emphasis on grades that this is valued more than the education itself. I've seen bright students that cheat because they feel overwhelmed. Because they know to get into the top colleges and top grad programs they need straight As. Strike that, they need a >4.0 GPA. They have to navigate the unknowns of which professors even hand out A+s, will forgo a better teacher for a teacher that gives more As, and so on. *They are not optimizing their education, they are optimizing their GPA*. Not because they don't care about their education, but because they do. Because everyone knows that the next rung of education is more important, so it is wroth forgoing some now to get access to more later. No one will say it out loud, but we all know even pretty mediocore students can play catch-up even up in undergrad and good students can do that in grad school. I'm sure if you randomly selected kids with GPAs >3.5 from high school and dropped them into your top universities you wouldn't see a big difference in outcomes[1]. I believe this stress is part of why some students just check out. But there is some aspect that is simple here: if grades didn't matter, there's no reason to cheat. I'm not saying to abandon grades, but I think it is worth reevaluating the system. I don't think patchwork solutions are gonna solve things.
All of this misses the entire point of education. Honestly, there's a larger crisis that's going on and it is that our world has just embraced Goodhart's Law as a good thing, not a warning.
[0] For example, that it is actually really difficult to punish cheaters. Any serious accusation needs serious evidence. Even more so when departments measure the amount of cheating by how many cheaters are prosecuted. That same metric hacking is why those students got Cs, just as much as it was that the chair was empathetic towards them. Part of that empathy being back connected to the importance of grades...
[1] Legacy students make this complicated but that's a whole other long conversation that mainly deals with connections.