The Classical Period has always been dominated by Haydn and Mozart, so why do we need to waste time with names like Boccherini, Hoffmeister, Beck, Dittersdorf, Cimarosa, Stamitz, Richter, Vanhal, and even Hummel? Let’s simply adopt the obvious solution: if the music ends in a minor key and uses chromaticism, it must be by Mozart. If it employs monothematic sonata form and has a sense of humor, it’s a lost work of Haydn. All worthy operas and concertos are Mozart’s; string quartets and symphonies are Haydn’s. In a pinch, if some doubt remains regarding attribution, we can always hedge our bets and say “Studio of Haydn.” After all, he had many students and lived a long life. If the music was composed after 1800 but before 1820 it’s by Beethoven unless it’s an opera, in which case it’s by Rossini or (when in German) Weber. After 1820 or so we have a brief window of opportunity to greatly expand Schubert’s output, after which no one except Berlioz, Mendelssohn, and Schumann wrote orchestral music that anyone cares about until the mid 19th century. Some eras are inherently tidy.
There's another related point, which is that we are more likely to like a work if it has a particular name attached to it. I know there have been times when I've been listening to the radio, hearing a not-particularly-impressive piece, only to hear at the end that it was written by Bach or Schumann or somebody inherently worthy of capital-R respect. Instantly, I have to fight the urge to pretend I really did like the piece I just heard. This is, of course, a function of not having enough confidence in my own opinions; like a lot of non-musicians, I don't really think enough of my knowledge of music to say with confidence that a piece of music is good or bad, so I look to critical consensus to get me off the hook. (An alternative dodge is to talk about the "structure" of a piece, this being easily analyzed. It's still a dodge because even if a composer has total mastery of the fugue or the sonata form or cyclic development, it says nothing about the quality of his inspiration.)
Of course, it's not only laymen like me who do this; Glenn Gould pointed out that critics tend to judge the quality of a piece of music based mostly on how "advanced" it is, and therefore in what period it was written. He described this as "Van Meegeren Syndrome," after the Dutch forger who got experts to believe that his paintings were by Vermeer, and therefore masterpieces. Applied to music, the syndrome would go like this, Gould says:
Some months ago, in an article in the Saturday Review, I ventured that the delinquency manifest by this sort of evaluation might be demonstrated if one were to imagine the critical response to an improvisation which, through its style and texture, suggested that it might have been composed by Joseph Haydn. (Let's assume it to be brilliantly done and most admirably Haydn-esque.) I suggested that if one were to concoct such a piece, its value would remain at par -- that is to say, at Haydn's value -- only so long as some chicanery were involved in its presentation, enough at least to convince the listener that it was indeed by Haydn. If, however, one were to suggest that although it much resembled Haydn it was, rather, a youthful work of Mendelssohn, its value would decline; and if one chose to attribute it to a succession of authors, each of them closer to the present day, then -- regardless of their talents or historical significance -- the merits of this same little piece would diminish with each new identification. If, on the other hand, one were to suggest that this work of chance, of accident, of the here and now, was not by Haydn but by a master living some generation or two before his time (Vivaldi, perhaps), then this work would become -- on the strength of that daring, that foresight, that futuristic anticipation landmark in musical composition.
And all of this would come to pass for no other reason than that we have never really become equipped to adjudicate music per se. Our sense of history is captive of an analytical method which seeks out isolated moments of stylistic upheaval -- pivot points of idiomatic evolution -- and our value judgments are largely based upon the degree to which we can assure ourselves that a particular artist participated in or, better yet, anticipated the nearest upheaval. Confusing evolution with accomplishment, we become blind to those values not explicit in an analogy with stylistic metamorphosis.
This applies to more than music, of course. How many times have you heard someone -- a critic, whoever -- praise an old movie or book for being "ahead of its time?" Works of art are often praised on the basis of having broken new ground, or introduced new stylistic devices. But does that really speak to how good they were, or just how different they were at the time? I once took a course in silent films with a professor who frankly disliked D.W. Griffith. People often asked him, he said, "But what about Griffith's technique?" To which he would reply that any technical advances of Griffith's were part of history, and had no bearing on the evaluation of the films as films. I didn't agree with him about Griffith (not about Broken Blossoms or Orphans of the Storm anyway) but I thought he had a point in general: innovation is essentially a historical matter, not an artistic matter. Or put another way, if we need to know that something was ahead of its time, then how interested can we be in the work itself?