When I read Anne's work, I don't really care if it's the UK or US edition. My spoken English is largely British, with a very slight Finnish accent, but I switched to US spelling online ages ago. I work as a translator for the government, and professionally I'm required to use British English (although whether that's still true following Brexit remains to be seen) so I'm comfortable reading both variants.
However, reading US editions of Dick Francis' or Agatha Christie's works is simply weird, and I made sure the Harry Potter books I bought were UK editions.
Regarding Shakespeare, Elizabethan English was closer to some modern US dialects than any UK dialect. Certainly closer than the posh English of the British aristocracy, in which it is often presented on stage or in movies. I'd love to see
Original Pronunciation presentations of some of Shakespeare's plays.