I still think you guys are missing the point of the "no scoring" rule. While there may be some hippies who really buy into the "nobody's feelings get hurt" line, that's not how the rule really originated.
I coached a basketball team of 5 and 6 year olds in a league where score was kept. The team was pretty short on ability as only one kid on the team, Jacob, had played before.
Well, everytime we were in a close game everyone would always just throw the ball to Jacob because he was the best scorer. Sure, we won more games because of it, but the other kids on the team didn't have the opportunity to work on their won skills like they should have becasue everyone was too focused on scoring.
It got to the point that the only way i could anyone else on the team to shoot, was to NOT let Jacob shoot in practice. So, because the kids were worried about the score they didn't get to work on their skills in games and Jacob got "punished" in practice for being ahead of the learning curve.
I've also coached team in "no scoring" leagues - baseball, basketball and one regretable spring of soccer - and while I had to put up with all the "what's the score, what's the score" questions, it was unbelievably easier to teach teamwork and get all of the kids an equal opportunity to learn.