I'm sorry, but I think there's something wrong. This is what you posted:
Quite a few linguists ( J Cheshire being one) state -------> that, even among
educated people, usage such as "There's lots of museums" is more common
that the grammatically correct "There are lots of museums". -------> How did
that come about? Why is the ungrammatical form more popular, even among
educated people?
Isn't that about the fact that "there's + plural" is very popular even among educated people?
Then I said I was not surprised, so the answer to your questions is: "I'm not surprised, therefore in my opinion it's normal."
So, on second thought, I would say I was completely on topic, LOL.
I didn't say "There are lots of museums" is not idiomatic, it IS idiomatic. But "There's lots of museums" is idiomatic as well.