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.
Are we talking about the same country? Most of those professors don't even teach if they can help it. Their job is to bring in grant money to the university. The others are paid hourly wages to be adjuncts, and I'm not certain it's accurate to say that they're "much higher-quality". But if it were, then perhaps that's your problem... the million k12 teachers you need are all teaching secondary education in temp positions for temp pay.
Always makes me think of The West Wing scene:
> Education is the silver bullet. Education is everything. We don't need little changes, we need gigantic, monumental changes. Schools should be palaces. The competition for the best teachers should be fierce. They should be making six-figure salaries. Schools should be incredibly expensive for government and absolutely free of charge to its citizens, just like national defense. That's my position. I just haven't figured out how to do it yet.
Video (sorry for the burned in subs, should be queued up): https://youtu.be/IzV09gESyh0?t=39