Depends...Do you want to get away from it all and enjoy sailing or do you want to keep your same habits that you have @ home. We like to get away from it all and relax. That's why we sail. It's peaceful and relaxing. You can get TV, news, movies anytime, but can you get a place where there's peace?
Absolute zero importance. A simple antenna will get you local stations, when you are in range, for news and weather, and to watch the occasional ball game. Otherwise, I go boating so that I can get AWAY from being plugged in all the time!
Really now, be kind. Those who are suffering from economic inconveniences and unable to hire a proper theater company to fill their theatres, may indeed find commercial entertainment electronics of some value onboard. And good booking agents are like all other good help, really hard to find.
Certainly not important enough to blow $5k on it, but if I bought a boat with one already on it, and was a full-timer, I'd probably use it.
We have a 12V 22" TV/DVD combo on the boat. It doesn't get used very often, but once the day's sailing is done, we're on the hook, we've watched the sunset from the cockpit, read our books...we'll enjoy a movie, or an episode or two of Andy Griffith or Hogan's Heroes (which is what we'll usually find on the only channel that comes in clearly anchored in the sound) just before bed from time to time.