I've noticed the same thing about the drop off from 10 - 12 ball to 13 - 14 ball.
When you move to the full 90' bases the game gets bigger and the kids who played ball because their parents made them didn't have to play any more.
Where I have lived 14 is high school age. Players have to maintain good grades in school in order to have the luxury of playing organized ball. They also have to maintain good attitudes in spite of the hormonal changes going on in their bodies.
There is less stigma in not making the varsity team as a freshman or sophmore than as a junior or senior.Playing 13 - 14 is more socially acceptable amongst teenagers. Playing 15 - 16 usually means that you didn't make varsity and are playing with the other 'rejects'. In reality, there are only so many spots on the varsity for whatever number of players trying out.
Kids that don't make the team have the option of giving it up or playing 15 - 16 ball.
I don't think that there is enough knowledge or publicity for the many baseball programs for 15 - 16 year olds in most parts of the country.
Most parents and children are not aware of such events as the Junior Olympics or the PONY World Series just to name a couple.
I think more kids would continue to play in spite of not making their school's varsity team.