This one supports at least a sloppy rationalization, to wit:
Shakespeare in English and Luther in German left extensive writings which had so many first-hand readers, decade by decade then century by century, that they acted as a kind of “sea anchor” – a drag that impedes drift. We need help really ‘getting’ Shakespeare, and doubtless Luther’s 16th-Century German is a chore to modern Germans, but both authors are still read by laymen and without translation.
So, that being the case, a) we know that 16th Century English sounded very different from what Australians, British, Americans, etc. etc. speak today. The accents differ, but we understand each other fairly well.
Second, successive generations of newscasters speaking to the nation every evening at 5:00 or 5:30 p.m. etc. also retard otherwise rapid shifting in the national diction and accent.
That being the case, the answer depends on just how much of the time the average citizen-on-the-street accesses recordings that are older than, say, a 1930’s movie reel.
I don’t think the Nightly News “sea anchor” effect will be all that much greater than the Bard and the Protestant have already been.