This is merely my point of view, maybe you have another, but for me dance is not a competition. I have experienced a few opposing opinions to this recently and I was quite surprised, especially as it was within the school environment.
I think it is vital that school remains competition free. Its a place of learning, which inevitably means mistakes. Don't get me wrong I think you should strive to be the best - but thats in relation to what you can be, not anyone else. Everyone develops at different speeds, and if there is an air of competition and pressure it could block people from taking in the information they need as they try to keep up. Its not easy to learn when you are stressed out.
Also, for me, the concept that the creative process is a competition is utterly ridiculous. Creativity is 'successful' because someone think it is. Someone else might think that the same creativity is unsuccessful. Creativity is also about the process it took to make work, which is not always visible in the finished piece. Creativity requires experimentation, which means sometimes things 'fail'. All these reasons mean that competition is out of the window. If people at a dance school want to be in competition perhaps they've picked the wrong profession. Try becoming an athlete, there winning and loosing can be defined by 1st, 2nd and 3rd place.
When I graduate and enter the real, tough, competitive world of dance maybe my view will chance slightly. But I doubt it. I've never been that competitive. I just want to make, and dance, good work and hopefully people will enjoy it.