It seems like it would be exactly analogous to the formation of pidgins, which takes one generation, not centuries. Also, if I think back to high school I would challenge the idea that every speaker of modern English has "no problems" reading 200-year-old texts.
People have been learning foreign languages in school without developing a pidgin for a long time now. Pidgin formation seems much more likely if the language acquisition is not as part of formal training, but from an informal need to communicate like for trade.
But often you're not missing meaning but simply context. Shakespeare is not hard per se due to the language but because its based in a world that is alien to you.
