There are lots of good thoughts here. I'm just going to address one.
Money.
When I worked in sales, one of the first things I was told is that a buyer's objections are never about the cost. Look at the US economy; people buy things every day that they can't afford. The AVERAGE American family owes more than they make. Being able to afford something has NOTHING to do with whether or not people buy it.
Case in point: For a while, I played an app based game called Castle Clash. It was one of those "freemium" games where you can play for free, but if you want to actually win you'll have to buy the extra items they sell. I never spent real money on it, but I knew guys who had spent $3000 (not a typo) and more trying to make the top 100. That's on an app based game that will likely disappear forever in a few more years. Of all the things that it's hard to get young Americans to do, spending money on frivolous things is not one of them.
What is a significant factor is perceived value. "Will this bring pleasure to me?" "Will others see this and envy me?" "Does this put me into the cool crowd?" "Will this help my family in some way, make my life easier, etc?"
Even among people who are into flying things, a significant number of youth don't perceive that the AMA gives them value for their money. So they fly in parks without insurance. Quite a few more don't perceive value in our hobby, although I can report that nearly every 8th grader that I have build a glider and fly it has a blast doing it. The interest is still certainly there.
IMHO, the solution is to go back to our roots. Teenagers will need their parents on board to buy an RC plane, get a club membership, and get transportation to the field for training and then flying. That's asking too much for many, because while the kid sees the value the parent may not. Look at how the AMA grew during its heyday in the 50's- free flight contests that developed into control line flying. If teenagers had access to free flight kits, and membership got them a club to fly with and qualified them for a contest circuit, the perceived value would return. A teenager with a little bit of motivation can scrape together the money for a free flight kit and the supplies to finish it, and plenty of parents would budget for it if they perceived it was educational. So maybe the AMA should focus on creating programs through community centers, Boy Scouts, school districts and the like? If the AMA could provide a turnkey program that those entities could buy and pass the cost on to the families, we'd have an organic way of developing those young enthusiasts into RC pilots who support their own hobby later on.