Punishment and reward proceed from basically the same psychological model, one that conceives of motivation as nothing more than the manipulation of behavior.
Those who know they're valued irrespective of their accomplishments often end up accomplishing quite a lot. It's the experience of being accepted without conditions that helps people develop a healthy confidence in themselves, a belief that it's safe to take risks and try new things.
The difference between a good educator and a great educator is that the former figures out how to work within the constraints of traditional policies and accepted assumptions, whereas the latter figures out how to change whatever gets in the way of doing right by kids. 'But we've always...', 'But the parents will never...', 'But we can't be the only school in the area to...' - all such protestations are unpersuasive to great educators. If research and common sense argue for doing things differently, then the question isn't whether to change course but how to make it happen.
Strip away all the assumptions about what competition is supposed to do, all the claims in its behalf that we accept and repeat reflexively. What you have left is the essence of the concept: mutually exclusive goal attainment (MEGA). One person succeeds only if another does not. From this uncluttered perspective, it seems clear right away that something is drastically wrong with such an arrangement. How can we do our best when we are spending our energies trying to make others lose--and fearing that they will make us lose?