I like to compare progress in gymnastics to an RPG.
Bear with me on this one.
For those who don't play RPGs, a core part of most RPGs is that your avatar gradually becomes stronger and gets better gear and abilities as the game progresses. Sometimes, by tackling a particular boss or dungeon, you can level up, or obtain some great item that will make you stronger and propel you forward in the game. But sometimes, you just have to grind; that is, you have to fight easy foes over and over, simply because you need more battles under your belt. Sometimes you just need to level up and there are no secrets or shortcuts to that.
In gymnastics, you gradually become more proficient, both at specific skills (the kip, the full, the yurchenko) and at more general skills (tightness, aerial awareness, flexibility). Sometimes, with a particular drill, correction, or equipment set-up, you can cross some threshold -- say, a new skill, or a dramatic improvement on an old one -- that will propel you dramatically forward in the sport. But sometimes, you just have to grind; that is, you have to do hundreds or even thousands of reps of skills you can already do.
What does all this have to do with private lessons?
Well, going back to our RPG comparison, you can think of a private lesson like a power-up. Something that gives you a little boost.
Any RPG player will tell you that having the right power-ups for some bosses and dungeons is extremely helpful. But sometimes you just need to grind, and when you're in a grinding phase, power-ups tend not to make much difference.
Sometimes a private lesson can be that little boost that gets a gymnast over the next threshold. But sometimes they just need to grind out a couple thousand more tap swings, or handstands, or (insert skill of your choice here). During such a grinding phase, the bang-to-buck ratio of private lessons is pretty low.
By the way, when I say thousands, I really do mean thousands. My quick back-of-the-napkin calculations lead me to estimate (rather conservatively, I think) that the average level 4/5 girl in my program has done somewhere in the neighborhood of six to eight thousand tap swings before doing her first flyaway, and they'll double that number by the time they get to giants on a competition rail.