We've been at two gyms, one of which offers privates and the other of which never has and likely never will.
The gym that offered them did so only when needed to nail down a specific skill that an athlete was super close to getting during practice, or if a kid was recovering from an injury or a severe mental block and just needed a little extra individualized work. They were respectful of the parents' time and money and only offered them if they felt strongly that it would truly help.
The other gym, where we are currently, does not offer privates, to my knowledge and I'm really grateful for that. I think as my DD has gotten older, the fact that privates are not an option has forced her to make a solid effort to be efficient during practice and to be somewhat braver too, knowing that that will be the only time available to get it done.
But to go back to your original question, at age 6, level 3, I would not do any privates at all...the time and financial commitment grow exponentially if she stays in the sport, and I would rather give her every second of non-gym time to do non-gym things.