Just looked at national champions since 2000 and some interesting stats.

-Out of 14 champions only 3 occurred after their head coach's 4th year. (Mack Brown won it in his 8th year at Texas and Saban won it in years 5 and 6 at Bama). I take this to mean that only 3 times in 14 years has a coach won the NC with his recruits. The majority of time, they win it with previous guys recruits.

-Here is the data
FSU 4th year
Bama 6th year
Bama 5th year
Auburn 2nd year
Bama 3rd year
Florida 4th year
LSU 3rd year
Florida 2nd year
Texas 8th year
USC 4th year
USC 3rd year
LSU 4th year
OSU 2nd year
Miami 1st year
Oklahoma 2nd year

Interestingly, the 90s were different as Bobby Bowden (FSU) and Tom Osbourne (Nebraska) had 5 NC's after long careers at their respective schools.

Not sure how this info relates to BYU/Bronco but it does suggest that fresh blood can sometimes be helpful. That being said I don't think Bronco should be fired.