I am on camp of "would this have be a positive improvement to the player experience?" I'm inclined to say no. As with all suggestions, the next question is, would this be a good way to spend limited developer time? I'm inclined to say it would not be.
Now that my realistic, negative Nancy opinions are known, I will say I like the idea of having a more friendly way of knowing my character's exhaustion level. That is an idea I can get behind, as that would improve the player experience, in my opinion.
Also, I don't know that bard song does anything for exhaustion, but there is a feat "Epic of the Lost King," I believe that does.
edit: Type of Feat: Class
Prerequisite: Bard Song, Perform 6 ranks.
Specifics: The character may spend one of his bard song uses to remove exhaustion from all allies (including himself) within 60 feet.
So, I was half correct. Not bard song, but tied into bard song uses.