The Coaches Circle was set up long ago as an endowment to provide the money to supplement the coaches' salaries. A significant part of their compensation comes from this source.
It may be a little known fact but Whittingham is by far the highest paid employee at the University of Utah, right at $2 million a year. In fact, he is the highest paid public employee in Utah. As are football coaches in many other states. It's become a very high paid job. The yewt DC, Sitaki makes about $500K. Assistant football coaches get paid pretty well too.
The perception persists that BYU coaches are far underpaid. However, Bronco has signed two contract extensions since his salary topped $1M a year. Each extension came with what BYU has said was significant pay increases. Bronco makes less than Whittingham but not as much less as people may think. The BYU assistants also make less than yewt coaches but again, not so much as people may think. BYU has stated that the coaches salaries are "Competitive." BYU is probably not in the Top 50 in program salaries but they aren't far below that.
BYU does not like the idea, for obvious reasons, of a football coach being their highest paid employee. Thus the Coaches Circle. BYU is not a state government, they seem to have taxpayer money to burn. BYU does not choose to do that. But they recognize that coaches must get competitive salaries. So don't let anyone tell you that BYU coaches salaries are not competitive. It's unlikely that a coach is going would be able to leave BYU for significantly more money somewhere else.