Sure, but the archaic language can obscure the awesome idea. "Why are you Romeo?" may sound less poetic to modern ears, but isn't that how people back then would have parsed it - just as easily as everyday language, because it was their everyday language?
I feel like in a way we're losing Shakespeare's intended effect, because we insist on using a "language" that isn't used anymore. Yes, I understand that it's considered the same language, but a language isn't really one thing, it's more of a spectrum without sharp edges. Shakespeare is much closer in time to Middle English (which is considered a different language) than he is to our time
True, but a big part of Shakespeare is the rhythm, and if you replace the words with newer words that disappears.
Not to say it will be a complete failure, but it does lose some of its poetry and power.
And smut. There's a lot of smut and double entendre in Shakespeare. An innocent modern word like "nothing" has multiple layers of meaning in Elizabethan English.
Modern audiences don't get it unless someone explains it to them.
I disagree. Shakespeare was not "plain" even in the 16/17th century. It wasn't archaic, but it was far, far from plain. The same is true for a lot of great literary works, even recent ones. Many great works have a lofty diction, which is easy to lampoon when inferior works veer into purple prose, but when it works, really elevates language.