I think the reason young folks aren't into it: it's a matter of kids looking down at screens, not up in the clouds. Maybe. I don't know.
Cost is definitely a concern, but like others said, people spend money on what's important to them. Yes, $240/hour for a 182T hurts a little, but damn is it worth it. Granted, it's probably cheaper in other parts of the country, but everything is adjusted for cost of living.
But I think we somehow need to promote the passion and the cool factor and all the good things about aviation. Most people just hop on southwest flights or read about GA crashes in the news. I will say... The neighborhood grade school takes kids to the local aviation museum at SQL... So cool!!! I think things like that are crucial.
It's not that younger folks are looking down at their screens so much as that private aviation is not of their generation.
I was born in 1957, my father was born in 1929. When he got out of the Air Force, he bought a half share of an Ercoupe, which interestingly enough was based at Chicago's Orchard Field, which we now call O'Hare International Airport. At that time, being a pilot was akin to what being an astronaut was when I was a child. Naturally, when I was old enough, I wanted to get involved as well. There were a couple of other guys at my high school who were also planning on getting lessons when they could, but not as many, percentage wise, as would have been in my father's time. Aviation had become more commonplace. Jump forward to today, and a smaller percent of the population is aviation minded.
It's not just flying that has seen this change. When I was a kid, it seemed like all the girls were horse crazy. Girls of my daughters' generation, not so much. Mine have gone for three trail rides in their lifetimes and they aren't clamoring for any more. Both of mine are dancers, but some of their friends are gymnasts, volleyball, soccer, and lacrosse players, and a couple are heavily into rowing. Girls of my sister's generation didn't play soccer or lacrosse at all. Times change, and things go in and out of fashion.
It's always been true that the vast majority of the population will not be interested in learning to fly. The only thing that has changed is that the percent that is not interested in flying has grown slightly larger. There were still something like 16,000 new private tickets earned last year, and just short of 50,000 student certificates as well, most of which went to people under age 30. Yes, I realize that some of these pilots are hoping to fly for a living, but there were 27,000 student pilots and 26,000 private pilots who were in their 30's last year, and I'm pretty sure most of these folks aren't planning to make careers of flying.
If you're really wanting to do something to make GA more popular, rather than trying to interest people who've shown no interest, you might want to figure out why only a third of those who earned their student tickets go on to get their private licenses.