I guess it's like how time travel always funnels them to one country.
And there's that. It's worse than that even – the Ancient Greeks were aliens, the Romans were aliens, the Native Americans were aliens and we even got Nazi Germans who were aliens. It's like those people and places never existed on planet Earth. To make several stories set in Ancient Greek setting, yet never ever visit the actual Ancient Greece down here, keeping it all in US-era North America? That's just not right.
Then again, holodeck Ireland was enough of an embarrassment, so one can be kinda glad they don't exist in Star Trek. And I doubt anyone would be doing this kind of time travel Trek stories any time soon, so whatever.
Besides, explaining why they spoke English in 16th century China would be even more difficult than explaining why aliens all over the galaxy speak English. They already confused that poor Japanese fellow enough with having Amelia Earhart speak perfect Japanese. I wonder, does the universal translator work for lip readers? I've been forever confused by how not only I hear English, but I see their lips move in English. And if they didn't, it would be a dead giveaway.