As a side note, in a way it's misleading to speak of Beethoven "overcoming" deafness. All of the master composers were so well-trained at their craft that they could hear the music in their head without "trying it out" on a piano or other instrument. By the time Beethoven was deaf being able to hear was superfluous as far as composing was concerned...
We know that Beethoven himself was tremendously depressed by the onset of deafness and thought of it as a terrible misfortune to be heroically struggled with:
But we also know that he gave himself excellent pep talks and then kept going for another thirty years, writing great stuff long after his deafness was far worse than it was in 1802. So, yes, it seems that Beethoven eventually came to agree with you!
And, come to think of it, as I remember Beethoven's biggest complaints about deafness centered on loneliness, and on his fear that nobody would want to hire a deaf composer. I don't actually recall him complaining that his work might suffer. So that's another point in favor of your argument.
Oops, too late to edit, but I forgot that when Beethoven wrote his Testament his fame up to that point had been largely as a pianist, with a healthy side order of composition. And I believe he might have expressed some worry that his piano playing might suffer... which in fact it did; history contains quite a few tragi-comic written descriptions of Beethoven's latter-day attempts to play and conduct.
But his composition just got better, so in fact his declining fame as a performer was balanced by his increasing fame as a composer.
Actually in a lot of his orchestral work, for example the 8th symphony, his arrangement was off. Stuff like trumpets being drowned out by other horns, etc. It's the kind of thing that would be hard to imagine without hearing it.
