It’s funny how predictable these speculations are. They work on this model: Drama was the hot form of entertainment in Shakespeare’s time, whereas TV (or film, or advertising, or whatever) is the hot form of entertainment in our time, “if Shakespeare were alive today” he’d be involved in our hot form of entertainment.
But what if Shakespeare was involved in the theater not because it was on the cutting edge but because he just loved the theater? After all, drama written and performed at a very high level continues to be one of the great human achievements, just as it was four hundred (or two thousand) years ago. And gifted people are still attracted to it, and will be for the foreseeable future. Maybe if Shakespeare were alive today he’d be an actor and playwright. And maybe — not as likely, I grant you, but maybe — Gutenberg would be involved in the printing business. We are too quick to analogize in these matters.