My parents played a lot of classical music at home, and when youngest brother heard a violin he would go get a frying pan and chopstick, and play along. Mom and dad would get to the symphony early so that we could sit in the front row (no assigned seats), and DYB was simply enthralled by the string section.
Your first sentence is the key. If a child doesn't listen attentively to recorded music at home, or when someone is playing, then they shouldn't go to a symphony. There certainly are children who adore live music, and later, we tend to call them 'musicians'.
In my home town, there was a woman who taught Suzuki, who observed that her son had a tremendous desire to play the violin. She had some serious connections in the music world, and her son got to meet a lot of musicians. He remembers meeting Aaron Copeland when he was still young enough that Copeland picked him up and sat him on his lap, and inquired what he wanted to do when he grew up. Brian told him, 'I want to play 'Rodeo' in concerts.' Of course this got a huge laugh from Copeland and the other adults!
When Brian was 12, he entered the school talent contest, and my mother was one of the judges. (Someone thought that having the science teacher as a judge would be more objective.
) When he came out on stage, her heart sank; she figured the audience was going to hoot him and his violin off the stage. Brian played 'Rodeo'. At the end of the piece, the students were clapping and stomping along, so much that Brian just paused a second, and started over again. Mom said that at that minute, she knew that Brian was already a professional musician- he'd known his audience and gave them what they wanted. For many years (and even now, so far as I know), 'Rodeo' was Brian's encore piece.