Last year, I never really did any private lessons for my boys during the preseason or season. I was asked but my life was just too hectic when they asked to figure it out in my fluctuating schedule.
I did ask one of my boys to come into open gym and if I had nothing to do, I would help them when I could. One of these days was only coming 1 day a week, maybe 2 days ( for level 4 ) because of other time commitments. If this boy didn't have the talent, I would not have allowed it as an option to work so few hours and be on team. He was coming from the rec program and I wanted him on team badly. He ended up getting a few 9's during the season and a 50 at state so considering how little he trained it was pretty good. I was also hoping he and mom would realize how much more they needed to commit to training hours if he wanted to be more successful and get on the podium.
I also did this because I felt it was my responsibility to get him up to speed as I asked him on team and it was my program. If I wasn't the head coach, I definitely would not have bothered. His schedule was pretty busy but at least he could come to open gym and get some routines in and I'd check them when I was done with my classes.
I've been known for years for putting in free time for gymnasts of mine. Especially if they had to wait for older siblings or had spare time. I've never really relied on private lessons being a significant part of my income or trying to make it so. I have preferred to spend my time with gymnasts who really wanted to commit to the training, with me, before I even committed to coaching them privately ( typically cheer tumblers, but on occasion promising rec/developmental kids or team kids ).
At one gym, which was a city gym, there wasn't really an option for privates because of how the gym was set up. Even in doing so, there wasn't any money to be made because the privates were through the city rather than paying them a percentage. If a gymnast was falling behind, we'd just ask them in when we had time off before or after gym. Obviously the optionals would pay for their routine choreography but I'm talking about compulsory girls, especially during summer dealing with vacations and all that.
Privates work awesome for routine refinement and getting skills, if everything prior is being done ( good coaching, enough hours, enough shaping and conditioning [ strength/flex ]).
OTOH, I was very concerned and peeved when a few of my team kids started doing privates with one of the gym owners ( who had coached them before me ) because there was some errors that popped up during competition and the kids dared to argue with me. I had to talk to the owner, my boss, about why I was doing certain things, like not going for bonus or this way. Therein lies the problem of doing privates without one of your primary coaches.