Also I don't think we can assume that teachers are able to give tutoring in all the levels the children might get too using the khan videos. You might say "how hard could it be for a 5th grade teacher to tutor trig?" but they like anyone else (including khan) probably would have to review some concepts (most teachers don't remember heron's formula by heart). This means they have to prepare multiple tutoring subjects at the same time. In one on one tutoring sessions that's easy but with a class of 25 children it can get quite hard.
It requires a rethinking of the way schools are designed I believe. Maybe have multiple teachers per class with each one specializing in a level to tutor. Classes would be bigger but you'd still have a similar teacher to student ratio.
Sounds great-- are you going to reimburse the advanced children for doing the teacher's job?
I also think that, unfortunately, America kids have an anti-geek attitude that could make tutoring difficult. The statement that "this kid is better than you, and now you have to listen to him/her" might not be taken well by some of the poorer performers.
I don't think the anti-geek attitude is as universal as you think. All through high school, I was the stuttering genius (I am pretty convinced that's how everyone saw me) who was terrible in gym and everyone loved me. I helped bring home academic challenge (quiz bowl) trophies and nobody ever picked on me. (I was class of 2002. Maybe it's generational?)
(I also had a younger brother who'd beat on people who might otherwise have picked on me. Nobody told me at the time, though. Whole situation was kinda weird.)
It requires a rethinking of the way schools are designed I believe. Maybe have multiple teachers per class with each one specializing in a level to tutor. Classes would be bigger but you'd still have a similar teacher to student ratio.