I would like to see badges in the trophy case. I can very rarely fully complete a challenge due to time but I always get badges. Today I just got the Specialized Spring Classics Challenge 1/4 complete badge. It would be nice if that went into my Trophy case. Every month I'm getting badges for completing 250km riding or 2250m climbing. But the badges just disappear down the news feed.
Any badge you get is an accomplishment that should be recognized and be in the trophy case. As you increased your riding over the month the badge would be replaced by the next one up. If you are comparing with your friends, one might have the May 250km badge and another the May 500km badge.