> Literature from before 1800, Davis notes, is ‘mostly unread, even by writers’

I strongly disagree. There are many counterexamples, some authors are still widely read. Besides Shakespeare, it's Defoe, his Robinson Crusoe is one of defining books for me, later I also enjoyed Journal of the Plague Year and Moll Flanders. Swift's Gulliver's Travels is in top ten list all of the books I ever read.

It's a bit hard for the casual reader to discover to what extent the spelling and punctuation, and perhaps more than just the spelling and punctuation, has been updated for modern editions of those books, but there are photographs online of the original 1726 edition of "Gulliver's travels" and it looks like the main obstacle to me reading it, if I could afford a copy, would be the way they wrote s as ſ, which is a trivial matter. The book is still worth reading and still fairly widely read, I would guess.

On the other hand, if I hadn't done Shakespeare at school and someone were to hand me a First Folio (1623) I don't think I'd make much progress with it. Of course most people don't read plays anyway.