>the "golden age" hypothesis (people in the past were better at innovation), the "bad taste" hypothesis (Beethoven and others don't deserve their reputations), and the "innovation as mining" hypothesis (ideas naturally get harder to find over time, and we should expect art and science to keep slowing down by default).

I think you're missing what I consider the most likely explanation: There are a lot more people in these fields now, trying to be the best. What's remarkable about these historical figures is not that they were better at what they did than people nowadays, but that they did it first. So I am not sure we'd notice a new Shakespeare. We'd simply lump him in with all of the other really good playwrights we have. Nothing would make him stand out as the best. 

So it's possible that our scientists, artists, etc. are better than these historical giants, but we just can't tell.