I agree that the most accessible way to get young people to experience theatre is not to put it on stage, but to bring it to the schools.
I'll never forget a powerful theatrical experience I had - directing the high school version of Les Miserables in a small Indiana town. A group of about 45 young people let themselves be immersed in the themes of the musical; and halfway through the rehearsal process, we lost a senior classmate to a tragic car accident. I can't even begin to describe how powerful the last scene was, when Cosette says goodbye to her father and he joins those who have passed on before him. When the show closed, I was looking at a group of 45 kids who LOVED the theatre, and who had been profoundly moved by it.
These were young people from the rural midwest, who had never been to Broadway, and would probably never step foot on the street in their lifetime. But they all eagerly watched the Tony awards that year, wanting to see the dance numbers and learn more about new shows. So I agree that the best way to grab young people and hook them on theatre is not to bring them to a Broadway show, but to give them a script and an empty stage, and let the magic take hold. Then, my friend, you have created a life-long love affair with the performing arts.