How unique is pay to play to soccer though? Seems like expensive travel teams are pretty common for volleyball, baseball, and basketball. Hockey and football have always been costly at high levels too. That hasn't prevented the US from having strong national teams in those sports. As far as what I see, expensive is the norm for youth sports regardless of what you play.
This is a tangent not super relevant to the OP, but national team success ALWAYS needs to be compared to its competition. Three big factors are participation, cultural importance, and infrastructure. I'll use baseball, men's soccer, and women's soccer as examples.
Baseball: The U.S. has huge participation, a long baseball tradition, and great infrastructure. But despite all of that, Japan, the Dominican Republic, Cuba and Puerto Rican national teams can all compete with the U.S., despite the U.S.'s huge size advantage. It's because baseball is undeniably the cultural king in those countries (from a sporting perspective). All have good baseball infrastructure (Puerto Rico and the DR each have a development academy from seemingly every MLB organization).
Men's soccer: the U.S. has huge participation numbers, but culturally soccer's behind 2-4 sports, depending on region. Multi-sport athletes tend to become serious in other disciplines, and there isn't a strong coaching tradition among parents and coaches at the youngest levels.
Compare this to Europe, where kid's are entering professional academies as young as age 3 (this usually costs them nothing). Soccer is the sport of their parents. Croatia and Iceland have far fewer kids playing soccer than the U.S., but produce far more talent (per capita, in Iceland's case). Soccer infrastructure and culture are far better there. Example: Iceland has a professionally licensed coach for every 1,700 people who live there. You have to have a pro license there to officially coach kids 10 and up, and they're all paid by the Iceland soccer federation.
Women's soccer: The U.S. is very good, and historically is the best team in the world. In the rest of the world, soccer is viewed as a physical, masculine game. (It sounds unbelievable to many, but it's true.) In men's soccer powers like Brazil and Germany, women's soccer wasn't given the infrastructure or support it needed until the 90's. Places you wouldn't think of as soccer hotbeds (U.S.A., China, Japan) are/were soccer powers, because they gave the women's game more resources than their peers. Soccer was/is viewed as a great sport for women in those countries. Now that more and more countries have devoted resources to women's soccer, the gap between the old powers and the Brazils, Germany's, etc. is closing rapidly.
European girls are now growing up playing in professional academies (again, for nothing), while most American girls don't have the opportunity. This spells eventual doom for the US women's national team. Participation numbers are nothing to a national team if they don't get the coaching they need. I'm not the only to predict the USWNT's decline in coming years.
Aside: if you're wondering where these countries are getting money for soccer, it's mainly from FIFA and World Cup revenues, along with federation dues from member clubs, which have revenue streams from their pro teams.