I would ask, why make a film about a composer to begin with? Or why make a film about any great artist? I think a film about the trials and tribulations of some nameless beat cop somewhere would be more interesting than a biopic about a genius. Think about it for a second, you're all composers, how would a movie about your life transpire? How do you think a film about, say, Albert Einstein, Van Gogh, or Shakespeare would play out. Unless you're a big fan you'd probably pass. Unfortunately, films about art geniuses have to be, 'embellished' so to speak, to attract a distributor. It's funny how you don't have to do a whole lot of embellishing when it comes to capturing the life of some loser serial killer for a film. There has to be something to pull a paying audience in.
William mentioned that somebody like Kubrick should have done a subject like Mozart or Beethoven. To be honest William, I don't think Kubrick would have touched it with a ten foot pole. He tried touching Napoleon, a vastly more dynamic life than even the most gregarious composer, and he gave up. It took him about 20 years but he finally gave up. Could you imagine Mozart through Tim Burton’s eyes?
I think Amadeus is one of the most misunderstood films of film history. After viewing it, most people conclude, "so Mozart was an obnoxious immature little punk. Hmmm! I didn't know that." As Erik pointed out, Amadeus is about Salieri and not about Mozart. Basically, Amadeus is about a pious composer who renounces his faith in God. That's it. The root of Salieri's jealousy is his belief that God chose, "this creature" called Mozart to be his instrument of beauty instead of him (Salieri).
In reality, the jealousy was probably the other way around but for a different reason. If my music history serves me correctly, at the time, German composers had to fight and claw for respect in their own homelands because nobility favored Italian composers. Why? Because they were... well, Italian. It's known that Salieri was hired over Mozart for some teaching assignments and Mozart was constantly in financial need. In fact in some cases, if Mozart knew Salieri applied to the same post he was considering, he wouldn't apply. I could see some jealousy being sparked there but not for Salieri's musical prowess that's for sure.
The funny thing is that when I read the title to this thread I thought you were talking about movies made about bad composers [:P] Now there's an idea. If it worked for Ed Wood, why not?