It's not just a pet peeve for me because music download sites are all organized on the basis of "songs," "artists," and "albums" which just doesn't work for classical music -- so it makes them hard to use, even if they have a decent classical section (which most don't). iTunes has about the best selection of classical (unless there's one out there I haven't found), though it's still pretty lame. They organize the music very broadly by chronology (baroque, classical, romantic, etc.), but they maintain all the features of the pop sites -- like "top sellers," which are always things like Pachelbel's Cannon. But having to navigate iTunes as though you're looking for a "tune" is pretty bad. I guess classical is such a small, small part of the business that there is no incentive to modify the classical portions of these sites to be arranged by "composer" or "piece" or "category" or anything else that might make sense to us.
Likewise iTunes on the desktop persists in organizing by "songs" and "albums" and "playlists." There is no easy way to organize classical music in a sensible way. You have to create "playlists" that contain all the music on an "album" which is a pretty typical way we look at things -- because the "album" will often contain, say, the entire Chopin etudes, and that's how we'd like to see it organized, not as a series of 24 "tunes" in our "library."
So my beef isn't with the naive use of the word "tune" to describe a "piece" or "composition," it's with the lame organization of classical music that results.