This scenario actually played out with my (at the time) 13 yr old son's competitive/traveling soccer team. Their regular coach had to step down abruptly at the beginning of the season for personal reasons, and the replacement/assistant was epically bad, with an 0-fer streak to open the season rivaling Cal's/Fox's. The parents revolted, the coach was sacked, and for several weeks, the kids practiced by themselves and played games without a coach (and only revolving parental oversight at practices and games.) I'm pretty sure that this would have been against league rules had anyone been paying close attention. But, given the relatively low stakes, no one outside the team complained. They started winning and then a young enthusiastic guy who wanted to gain experience coaching youth sports eventually took over on the cheap. The team ended the year on a six game win streak, against the teams that had crushed them earlier in the year.
It worked because the kids, even though they were only 13, fully embraced the leadership challenge They spontaneously organized the drills that they remembered from the prior years in practice and designated on-field leaders for each game. I have no doubt that Cal's current players could do exactly that. Also, revolving oversight could include ex-players (e.g. Lamond Murray, Jerome Randle, etc.) who might not want to coach permanently, but, for a day or two...why not!
I say go for it! If this strategy raised revenue on top of that, all the better.