The idea of winners and losers comes from social darwinism, which is just another justification for people to keep wealth to themselves and not pay taxes "because it helps the weak".
The reality is that we truly don't know what motivates people to work or to innovate. That's why equality (not egalitarianism) is important.
> Getting lazy because of a win or quitting because of a loss will severely impact someone for their entire life.
Well if you look into society, that happens all the time. And even when it doesn't happen, people still put social filters on each others because of that belief. It's becoming a club of people which believe in "strong motivation".
> I think it is important to have competition early and often in life because learning how to win and lose is an important life lesson.
What kind of life lesson is that ? On what sort philosophy does it stand on? That sounds like a motivational religion.
The life lesson I got from it was that winning leads to social exclusion, from both peers and teachers. So yes, I learned to not (openly) compete any more.
I think it is important to have competition early and often in life because learning how to win and lose is an important life lesson. Getting lazy because of a win or quitting because of a loss will severely impact someone for their entire life.