Why So Few Excellent Teachers?
Since I have a fair amount of experience in higher education, I will venture to answer this question. One obvious reason is that teacher salaries at the K-12 level generally are not that great. However, even when the salary is good, the rewards for excellence tend to be disproportionate to the excellence. That is, teachers often get out far less than they put in.
Interestingly enough, one drain on the pool of excellent K-12 teachers is probably higher education. If someone loves to teach and has excellent abilities, they will quickly realize that the college/university level provides far more return for the effort. The pay, status, facilities, and benefits are generally much better. The problems are far less. In my own case, I did a stint as a high school teacher. While I love to teach, running study halls, dealing with discipline problems, and so on all made the job more of an ordeal than a pleasure. So, I did the obvious thing and became a professor, thus keeping the best aspects of being a teacher and ditching most of the bad ones.
Another obvious drain on the pool of excellent teachers is that someone who has the virtues needed to be an excellent teacher (intelligence, knowledge, leadership, creativity, charisma and so on) can excel in other fields that generally offer far more to a person. Such an amazing person could start her own company, have a high paying and rewarding career, or become a major force in politics. While some people do find the rewards of teaching to be sufficient, obviously enough most people with such excellence do not. They seek other careers and far greater rewards.
While it is tempting to say that such excellent people should be suitably rewarded (bribed) into going into K-12 teaching, there is the obvious question of whether the resources spent to get such stars would yield greater benefits than spending the same resources to get more average teachers. While sports teams can often afford to pay stars cosmic wages, there are actually very few professional sports teams while there are many, many schools.
Of course, improving salaries and fixing the problems that make teaching K-12 unpleasant can go a long way in improving the quality of education. This might well be better than trying to take a star approach.
Another reason why there are so few excellent teachers is that there are relatively few truly excellent people. After all, think about your own general experiences at stores, work, and so on. How many truly excellent and amazing people do you know? Of course, I suspect that one reason why we have few excellent people is that our educational system has some serious problems. This creates a rather unfortunate problem: we need a better education system to get better people, but we need better people to have a better educational system.