It's not a for profit enterprise. If someone invests it's for access to promising new players not for money from parents. Decisions get made based on talent, discipline, personality and sometimes your parents connections but almost never how rich you are. Some coaches do take bribes but they keep it on the low. American sports do it openly and it's almost universal.
The most relevant bit to your question:
> Ajax operates a fleet of 20 buses to pick up the boys halfway through their school day and employs 15 teachers to tutor them when they arrive. Parents pay nothing except a nominal insurance fee of 12 euros a year, and the club covers the rest — salaries for 24 coaches, travel to tournaments, uniforms and gear for the players and all other costs associated with running a vast facility. Promising young players outside the Ajax catchment area usually attend academies run by other Dutch professional clubs, where the training is also free, as it is in much of the rest of the soccer-playing world for youths with pro potential. (The U.S., where the dominant model is “pay to play” — the better an athlete, the more money a parent shells out — is the outlier.)
While Little League and local/Pop Warner support baseball and football on public/private funds, LOVB is doing the same without taking any money away from the public through school taxes. Softball travelling teams have been following this exact playbook for years, sucking up every dollar from the parents.
Build it and they will come. None of major sports markets are held for public interest.
That's like saying "I'm curious to know how the military is any different from a private military other than where the money is coming from." I'm sure you can figure it out.
EDIT Oh balls, I'll just tell you: poor people priced out; rich people win again.
The people that can afford to have their kids play hockey and other sports are usually in the top 10% of the income distribution which spends over 50% of the money in the US.
It sucks that youth sports can’t just exist without a PE shop extracting every dollar they can from parents, but that’s capitalism I guess.