What would be the meaning of competing without earning blue ribbons?

The only benefit is to get a higher score. If you are not earning blue ribbons for the league, you won't see the game graphics of the ribbons being totaled. So you will be able to play a little more overall, than those who are earning ribbons, maybe as much as a couple of minutes. This makes a bigger impact to Magic Eye users in Spot the Difference where a few seconds can allow you to earn tens of thousands of points.