I think the bigger problem is that teacher's unions have created a calcified public education system that is risk and change adverse. Hard to experiment with new ideas in that environment.
Child from the 80s here. I've had just about every teaching method crammed down my throat through the 90s. This includes more homework, more lectures, socratic desk arrangements, independent study, peer review, group work, class review, and many others I care not to remember. I have never heard any teacher say, "my union asked me to do this." And, usually, it was some teacher or principal working on their MA or Ph.D that had to invent a new teaching method.
So far the only thing that works consistently is listening intently, sitting down quietly and banging out the work, and raising a hand for assistance when your stuck.
And that is how it's been done for 100 years. It may seem calcified to you but the rest of the world uses it while the US tried all types of new-age teaching methods.
I would wager the bigger problem with schools is bad, obnoxious students. The classroom bully that disrespects the teacher, disrupts the students and gums up the educational experience for everyone. They used to be kicked out of school but that became illegal, then they were put in detention, but a chaperone costs money. Now it's left to the teacher to be educator and babysitter to some asshole.
In fact if anything, my personal impression is that the teaching method itself is among the least important factors; if everything else is in order, kids are going to learn no matter what teaching method you employ.