The older I get the more I enjoy classical music. Before I started to listen to it regularily I actually had to tear down some of the walls you mentioned. I felt old and weired listening to classical music in a world full of very catchy pop songs like "Shut up" by the Black Eyed Peas for example.
Now I really like it, I especially like organ music and choirs.
Did you by any chance hear about that modern music does not have any real harmonies anymore but classical music does? I got this theory by a former DJ. He claims, that in modern music (pop, rock, jazz etc.) the harmony can not be singeled out anymore, because the rhythm of the bass is layered on it. He says, the songs thereby do not have an inherent logic anymore, we are not guided through it in a logical but emotional way. Well, I don't know, if this is true, but many composers like Bach wrote very "logical" songs, I heard. Anyway, I also think that children nowadays could profit from listening to classical music. In my view it sharpenes the mind a lot. I always felt very stimulated by it.
PS I: When I am back on my PC I'll send you a link with the source of the thesis I was talking about. It's in German though.
PS II: Here's the link to the source of the thesis: https://youtu.be/e2xUiawGGoQ?t=219