Our nation needs something on the order of millions of teachers. Competition for the best teachers would work great, if you needed exactly 1 extraordinary teacher. Or even if you needed a dozen. But when you need 40 teachers or more per school district... you're going to end up with alot of mediocre teachers, and more than a few godawful ones.
And, I suspect, that the thing not even extraordinary teachers can do is give a shit. Some teachers give a shit about some students, a few give a shit about many/most students, but even those few will falter in a career that lasts long enough.
Any why do they even want this silver bullet anyway, as impossible as it is? Why would you want a trillion dollar boondoggle that can't possibly ever work? The answer for that is downright frightening.