I think there's a problem with the Shakespeare example. Shakespeare didn't write Hamlet to be played by Danish actors, and he knew very little about Denmark. He probably knew a bit more about Italy, but he didn't write Romeo and Juliet for Italian actors. There seems to have been very little attempt at verisimilitude in anything (hence the argument that the traditionalist choice in Shakespeare is modern dress as it seems Shakespeare's company pretty much wore Elizabethan garb no matter where or when a play was set, with perhaps a few exceptions).
Having said that, I generally agree with you.
But then . . . what about the Irish? It seems like in plays with Irish characters and even with Irish-American characters, we often get casts in which most actors are of Irish descent, but this doesn't happen so much with Italians or the Swedish or Russians or Germans or Jews. And as a Jew, I think of Jewishness as an ethnicity.