There are probably as many experiences with private lessons as there are gyms. Too often I've seen them used to compensate for inadequate regular coaching. To the extent that they are regularly needed, it suggests a flaw in the class structure...a child might be at the wrong level, a coach might not be spending time on the right stuff, the parents might be causing the child to miss too many practices, someone might have unrealistic expectations, or any number of other things.
When our current coaches wanted my daughter to work on something, they asked her to join in for a few practices with another team level class that was working on that. No privates, no different money. Current gym really only does privates for choreography and for cheerleaders trying to acquire skills before HS tryouts. If a team girl feels the need for extra, the staff tries to figure out why the scheduled 18+ hrs a week isn't cutting it. Since the girls are working on individual skill sets anyway (it's the Optional team), there's plenty of opportunity for each to work on whatever needs work, with the coaches spreading around to everyone.