Coaching staffs are often wrong about personnel decisions or are internally conflicted, i.e., head coach, O coordinator, QB coach all have different opinions or goals. I wouldn't be shocked if there were a couple coaches on the staff who quietly believe PJ should be on the field with that arm.
Pulling a QB that is clearly underperforming for a backup (Winbush/Book) or rolling with a hot hand after an injury (Zaire/Kiser) is different than evaluating talent in practice and making a the decision to go with unproven potential over proven above average play (Bryant/Lawrence at Clemson).
Fans and the Clemson staff as mentioned above. Georgia rolled with Fromm over Eason, Bama benched a title winner in favor of a freshman, Texas went with Ehlinger over Buechele (this was a bit more complicated), etc.
Often the reason is that coaches, like most people, do not like to take risks. Book is the safe play here. He's a good game manager and a proven winner. He's the guy that's going to manage the game against Virginia and allow your defense a chance to takeover. He's not the guy that's going to connect on a couple throws to win the game against Georgia. PJ is probably the guy that may force a few throws against Virginia, giving them a chacne to put the game away before the defense takes over. However, he may also be the kid who makes a few difference making throws against Georgia too.
If you're Kelly, 11 wins with an average starter is probably better than 9 wins with a risk taking gunslinger.
Overall, you're right, the staff knows more than fans. That's obvious. What's not so obvious is the coach's end game, the degree of separation between two players, whether their is dissent among the staff, team etc.