As a former rugby coach, the unfairness of being 'left until last' in a sports team selection process, is a practice that should be avoided.
Haimish I once taught in a school where the principal was only interested in sporting TALENT. Even the student of the yearaward (last year of primary), was always awarded to a sporty student. In one particular year I suggested we look beyond sport. I was not popular. Looking back I wonder if he was realizing his personal dreams through these students.
You're right about sport being about participation and enjoyment. For me, running was the best because I was competing just with myself. But it was also about realizing that I was quite good at something...and badminton...in my last year of high school...finding a little bit of ability was a little like new cream rising to the top. We played badminton while the others played netball, rugby and hockey. More importantly, because we didn't have to compete with the top dogs, we were confident to take risks. Isn't that what learning is all about?