The Olympics do not operate Olympic football. FIFA does. The Olympics have contracted out the operations and administration of each sport to its respective international federation. That's why Olympics football is run by FIFA.
Problem is, FIFA also owns the World Cup and is a huge cash cow for them. If Olympic competition were to be on par with the World Cup, FIFA stands to lose a lot of money. That's why FIFA installed the under 23 rule -- to allow countries to enter promising young talent that should offer very good, but not great, play. If you want to see all the best players, you have to wait until 2014 for the World Cup.
Incidentally, each team is allowed to exempt three players from the under-23 rule.
http://en.wikipedia.org/wiki/Football_at_the_Summer_Olympics#Changes_and_developments
BTW, I think I heard FIFA claim this rule is in place to allow the best emerging talent an opportunity to shine. However, they failed to mention why this rule only applies to the men. Women's teams can be made up entirely of players over 23.