I find myself very ambivalent here. I feel if children do not want to compete they shouldn't. but, but, but.... I was no good at sport, illness, dyspraxia and poor eyesight did for that, but I did enjoy the pressure that it put on me to really do my best at whatever it was and to enjoy knowing I had beaten my personal best or, for me, done really well, even if I knew I did not stand a cat in hell's chance of winning.
I think the problem is that whenever we think about competition, we think of winning and losing when perhaps we should look at it in terms of personal challenge. I can still remember very clearly and delightedly those odd one or two occasions when for some reason I actually did do quite well at some unexpected sporting activity.
The argument against competition is that it disheartens and undermines the losers, personally, I cannot remember ever being particularly bothered about losing and i wonder whether the child simply reflects the attitude of the adults round it.