I don't buy it.
I didn't pay attention in class for most of my school time and that was before any of the more modern distractions existed.
To do well in school, you need to:
1. Capture and memorize factoids that will be on the test
This can be done the roundabout way by taking notes, which does help with memory retention. It's however far more efficient to just copy other more diligent people's notes and memorize those.
2. Understand mechanisms and systems
This requires you to work on your own, try things, figure things out, getting error feedback. Schools are notoriously awful at this, with 20+ kids you just can not spend the time to give meaningful advice, to give enough feedback in a timely manner. You send kids home with homework and they get results a day later or worse. The kids that do really well here usually get help from parents/siblings/externals.
Neither of these require teachers to do any classroom work.
Of course, there's the whole social and daycare aspect of schools which can be beneficial or oppressive, depending on the teachers and environment. Let's just not pretend that actual learning needs a classroom environment, or that it's better in classroom environment, because we don't actually know that yet. Classroom teachers talking their book doesn't help.