Failure also produces a lot of false negatives though, I've failed at a lot of things not because I was bad at them (though, lord knows I have enough failures because of that), but because of bad luck, or bad instruction, or what have you.
There's a fine line between teaching children to learn from failure and allowing failure to discourage them inappropriately. The solution is to walk it carefully, not stay so far away from it that people never learn to persevere.
I can't say if the methods being used today to give kids "self-esteem" are misguided and/or ineffective. But I can say that the entire point of true "self-esteem" is exactly so that failure is perceived as a learning experience and not a discouragement. Genuine self-esteem needs to be the backdrop, regardless of whether or not "medals and rewards for everyone" are entirely the wrong way to achieve that.
Edit: I think what I'm trying to say is that there's a difference between self-esteem and self-entitlement.
As for Berra, the only reference I found was a claim on wikipedia that he was kept off the Cardinals by a team president who was moving to the Dodgers and was hoping to sign Berra there. [2]
These examples certainly don't mean that there are no false negatives when it comes to failure, but I think it's interesting that these two famous stories about great players overcoming early adversity are bunk. It is probably the case that most people start out not being so good at something, then gradually get better, with any early success compounding over time.
[1] http://probasketballtalk.nbcsports.com/2012/01/11/the-man-wh...
The problem is the distortion of your judgement from people who believe no one should fail (or excel really). It makes you not trust your own gut reaction.