There's never really been any money in poetry for people who were just published poets. "Great" poets were all subsidized by patrons, worked in odd jobs or other mediums, or died in penury (sometimes all three)! The same is true now as it was 200 years ago.
And even now we have spoken word and slam poets that sell out clubs & college gigs, and make ends meet on that. They are profound exceptions. And, also, Shakespeare's profits would be almost entirely due to his plays.
We can make a comparison with stand-up comedians. The majority don't make anything from it and a very large number don't even have any professional aspirations.
Yet, professional comedians make good money. The best are multimillionaires.
The developments the author points out aren't exactly new or exclusive to this century. You can trace them back to the Industrial Revolution. The 19th century English novelists I read seemed to populate their novels with characters who did nothing but drink tea, read books, make smart quips and over the summer, play a game or two of cricket (hallmarks of the quintessential Victorian gentleman, I was told). You had people who read as a hobby, and people who 'read' (and write about their reading) as a vocation (Matthew Arnold comes to mind, as do an unending list of independent lexicographers, researchers, and scientists).
Yes, but those are taught because they have a modern perspective which you won't get from Shakespeare. And it is hard to say that contemporary classics will last 300 years if you keep them locked under copy-write the whole time.
My point is that a world with Shakespeare under perpetual copy-write is different enough from this world that it would be very difficult to predict whether or not it would retain its status as a teaching necessity. It could very well be the case that we would be teaching modern renditions of folk tales instead. Or that someone else would write Shakespeare-style archetypes in a more accessible format, and we'd use that instead.
Everybody knows Shakespeare because everybody knows Shakespeare. Its hard to say exactly how much of that is undone by copy-write.