Kids are competitive WELL before age 12. Heck, they want to win when playing Candyland at age 4. But I still say it comes down to the emphasis placed on the kids by coaches and parents. It should NOT be "winning is everything". If it is, there's something wrong.
I have 3 kids and you should see us on family game night

I don't disagree with you at all, but the reality is (at least here for baseball) winning takes center stage for players, coaches and parents by the time kids are 12. A newcomer will get the minimum play time, the focus will be on the kids who are very good (or on the coaches kids). Its just how it is.