Of course it dies out. My town in CT killed the kids feeder programs when I was young, I never learned, and by the time I got to high school that high school program closed too. Somers High, CT. Last supported team, 1985.
Without you programs, like Pop Warner and SAFL where I am (Springfield/Western MA) kids get no chance to love the game when they are young. Playing is not as fun later, and there is a LOT to learn about everything. When you get into teaching and coaching, you see how hard it is to get kids to get into it.
If you want them to love the game and stay in it, they need a chance to learn it, tackling safely when they are wrapped up in pads as large as they are.