Many would say yes, but in this age of television it seems less and less important in our comfortable Western society. But if we look to some recent examples, we can see that theatre does indeed matter, matter to more than just eager actors too!
In the not too distant past, people have been killed, murdered, executed, expunged for their theatre work. Meyerhold, Russian director was so dangerous to his government, that they didn't just kill him, they expunged him, they brutally tortured and murdered him, took all the things from his house, threw his wife out onto the street with them and moved one of their officers into the flat, a if he had never existed. Expunged. So dangerous to the government were the simple free thinking ideas that had. He wasn't just killed, his violent expunging was meant to be a message to all, do not go against us.
The spirit of theatre and why it matters I believe is within this story of Meyerhold.
Longer answer: Live theatre has an immediacy that even the best movies and TV can't capture. Watching human beings create a new reality before your eyes is as close to magic as real life can come.
Yes, there are a lot of really bad plays out there, and yes, it does seem that we live in an age that doesn't have a Shakespeare. (although I think Epictetus may take exception to that, as a David Mamet fan. )
Let me put it this way: two weeks ago, people gasped when I put a gun in my mouth in A FEW GOOD MEN. And I'm not even a very good actor!
Another anecdote: I had the pleasure of meeting Steve and Maureen Van Zandt last year. (He plays Silvio on THE SOPRANOS, and she plays his wife.) Maureen told me that as much as she admires David Chase and the other writers of THE SOPRANOS, "it's not O'Neill or Williams or Shaw." (Her words, not mine - but I agreed with her completely.)
For emotional involvement AND intellectual stimulation, you can't beat theatre.