Services. Services, services. Services, services, services.
Sorry. I was just experimenting with what the constant use of the word services would entail.

More seriously, I think you're onto something here. There are two models I've seen for what a club is -- a loosely-affiliated collection of teams and an organization that provides services to children. I'm sure that there are infinite shades of gray here; but for the most part you can tell by asking a few questions to which model a club adheres.
Take RIIIPL-East participation. There are two ways to view this; a team earns the right to play the next year in RIIIPL-East or a club earns the right to create a team in a specific age and gender bracket to play the next year in RIIIPL-East. If you're operating under a model of a club being a loosely formed collection of teams and that teams are formed socially, then the former view holds sway. If you're operating under a model of a club providing services, then there's going to be an open tryout and based solely on merit a team will be selected that plays in RIIIPL-East based on the previous earned right.
To answer you specifically, there's no way in the world I could list "all" services a club needs; it's like asking any other business to list "all" the services it might potentially provide. I can certainly give examples. Enabling kids to participate in USSF Academy or RIIIPL-East is a service to those kids that Bridge decided to provide. Providing recreational soccer is a service. Providing various levels of competitive soccer, not just at the classic, challenge, and premier levels -- but high school preparation, and social soccer (where the focus is on playing with your friends) are all services. Programs where you scrimmage colleges are services. Showcase events are services. Tournaments can be services. Help in the college recruiting process can be services. College combines can be services. TOPSoccer is a service. Types of training (Coever, etc.) are services. Open training is a service (where you open up all training to anyone in your club -- or even people outside of your club.) Organized ride sharing is a service, particularly when part of a program to reach kids that might not otherwise be able to play.
Please note that I tried to use the word "service" as much as possible above.

In South Carolina today, I see threee youth soccer clubs/alliances that are focusing on top-to-bottom services for kids: CESA and CUFC and the Bridge alliance. Please note that this not not solely determined as a function of size; for example, LCSC and MPSC are large "select" soccer organizations that operate more under the model of a collection of teams.