Yes, and we're talking about statistically measurable things. There is plenty of room to experiment with different reward systems in competitions. For example, in Finland, there is an alternative figure skating judging system for kids' competitions, and they have medals (1,2, and 3 place), but everyone else is the rest. Thus they send a positive competence signal to the winner and a relatively weak negative competence signal to others (i.e. no one is labeled "worst", plus everyone gets some prize reward).
Tennis' Play&Stay program for kids under 10 years old is also a good example – they use different tournament structures, so no one feels like they lost.
Focusing on winners only is a societal choice though. I have met people (in countries were a lot of people like doing sport) that were practicing a sport and joining competitions for years even though they were not very competent in that sport - because it was their hobby and they just enjoyed being there.