I can only speak from personal experience (as a softball player and a private instructor for softball, but I think it still holds the same weight).
I think deciding on getting a coach really depends on the player's goals. If she is planning on playing competitive basketball for a while, perhaps even through high school and into college, a private coach will give her the edge she needs over her competition. Rec teams and/or school teams are great, as they offer the fundamental building blocks to sports, but with so many kids that signup for the teams, it can be hard to give individual attention to every single player. Also, some coaches may not be incredibly knowledgeable about the sports beyond the basics.
I played softball since I was 4 and had a private coaching since I was 11. That helped me become a better player (and no, I wasn't the worst to start!) and I eventually earned a scholarship to a DI school. Now, I know that's looking WAY ahead, but I just want to give you an idea of the impact private coaching had on me. As a private coach, I have girls as young as 8 signing up to learn how to pitch better, how to hit better, and even how to throw. These are all things the girls will learn on the field with their rec teams and school teams, but with me, they wanted more attention to the little details, to make sure their form is perfect. It's not like they are planning on playing college ball now (maybe they are, I haven't asked), but they'll at least enjoy the next few seasons a lot more because they'll be more successful.
So in short, the answer is no - it's not a waste of money. Even if it's only for a few seasons, knowing how to play and not being uncomfortable on the court and not lacking confident will probably make her time spent playing the sport a lot more rewarding and fun. If it's for a single season, you might want to hold off until you see if it's worth the investment, but that's all up to you.
Hope this helps!