Yeah, Borges' story is very clever, but part of why it's funny and intriguing is that in fact no one would react as Borges-pretending-to-be-a-critic-writing-about-Menard does even though there's an argument of sorts to be made that they should. And, actually, if someone were really able to make a robot that could regenerate Beethoven's symphonies (but nothing else) from scratch without having the equivalent of the actual symphonies wired in, that would be really interesting. Anyway, we digress.

I don't think the factors you list give sufficient reason to expect that there are people writing Beethoven-like symphonies as good as Beethoven's. Countervailing factors:

• Most of those people aren't steeped in the same tradition as Beethoven was; they will (of course) have more exposure to music that came after Beethoven, and less to (most) music that came before, and their training will have been shaped by everything after Beethoven, etc., etc., etc. (They didn't do as Menard did in the Borges story!) So the music they write will not naturally come out like Beethoven's.
• Most music-creators these days aren't trying to write Beethoven-like symphonies. The great majority of music-creators these days aren't even working in the classical tradition; most who are aren't writing symphonies; most who are aren't emulating Beethoven. (And I will hazard a guess that the most talented ones are particularly unlikely to be dedicating their talents to emulating Beethoven.)

Everything people love about Shakespeare is considered bad writing today.

Those things aren't considered bad when Shakespeare does them, nor when other rough contemporaries of his do them (so it's not just that there's a special case for Famous Shakespeare). Pinter's plays are pretty stylized and he won a Nobel prize. There's a big (albeit ridiculous) monologue in "Waiting for Godot" and no one seems to object. T S Eliot got away with writing a couple of plays in verse and I'm not aware that it harmed his reputation.

It's perfectly true that most plays these days aren't written in Shakespeare's style, but I don't think it's because that style is considered bad. It's just not what people do nowadays.