Now, the future of the rivalry is tenuous. The Utes will play in Provo in 2013 and will host the Cougars in 2016, but no other games have been scheduled, Hill said.
He said he was "being cautious" in making any assumptions about future scheduling, noting the Utes have "new opportunities" as a member of the Pac-12.
"What we have to do is make sure we don't come close to overscheduling," he said.
In Hill's mind, playing both Michigan and BYU in the same years would have put the Utes in that situation.
"I can't expect us to play 11 really, really difficult games in a season," he said.
The Utes, who travel to Michigan in 2014 and host the Wolverines in the 2015 opener, viewed dropping the BYU game as the easiest solution.
"The reality is, we have an unusual opportunity and we had to do what was best for the student-athletes," Hill said of his decision to schedule Michigan and not BYU.
So what of the future? Expectations are Utah will get more opportunities to play top-tier teams now that it is a member of the Pac-12.
With nine league games, the Utes don't have much wiggle room in their scheduling, particularly since Hill is intent on not overdoing it.
The 2014 schedule already is challenging enough, with Pac-12 road games at Arizona State, Colorado, Oregon State, UCLA and Washington State. The home games are against Arizona, Oregon, Stanford and USC.
In 2015, the Utes play home league games against Arizona State, Colorado, Oregon State and UCLA and are on the road at Arizona, Oregon and USC. The sites for games against Cal and Washington have yet to be determined.
Hill said he plans to stick with his nonconference scheduling formula of playing a top-tier opponent, a mid-tier foe that the Utes should beat if they're playing well and an FCS-type or lower-tier FBS opponent that the Utes should beat relatively easily.
"That is kind of the standard" for most BCS teams, he said.
While he said he considered BYU a top-tier opponent, Hill said it's not his priority to ensure the slot goes to the Cougars. Hill acknowledged Tuesday the Cougars had a different view.
"We know they aren't happy," he said.
BYU athletic director Tom Holmoe didn't try to hide his disappointment Tuesday, but he expressed hope that the series will resume on an annual basis after 2016.
"As a former player and coach, I love the BYU-Utah rivalry. It is one of the great rivalries in all of sports," Holmoe said in a statement. "There is so much history and tradition in the game. I understand that Utah has some challenges with scheduling, but as I have indicated on several occasions it is our preference to play the game every year. In the future, I know we can find a way to make that happen."
That might be overly optimistic. The Pac-12 and Big Ten have reached an agreement to play each other regularly starting in 2017. While Hill said he isn't sure how iron-clad that agreement is for annual meetings, he said scheduling remains a complicated task, too complicated to make any promises involving any teams even BYU.
The Utes lead the series 52-31-4 all-time. While the rivalry is one of the longest in the country, it showed no signs of lessening in competition, with five of the last seven games being decided by a touchdown or less. Utah coach Kyle Whittingham is 4-3 against the Cougars since taking over the program in 2005.
However, the competitiveness on the field wasn't enough to sway Hill, who says moving the game to September from its traditional November slot already seemed to lessen the importance of the rivalry.
"The reality is, now we are both in different leagues and everything has changed," he said.
The Utes cleared the way for Michigan by buying their way out of their planned road trip to Utah State for $500,000.
The Utes, who play in Logan on Sept. 7, likely won't make any return trips to Utah State, Hill said.
"It's hard to predict; it may happen one year, but I don't think so," he said when asked about possible future road trips to the Cache Valley.
The Utes have agreed to a four-game series with the Aggies in basketball, with Utah hosting the Aggies in 2014 and 2016 and playing in Logan in 2015 and 2017.
Hill also expects Utah's basketball rivalry to continue with BYU.
The Utah-BYU rivalry
• Teams have played annually since 1922, except for 1943-45, when BYU didn't field a team due to World War II.
• The Utes lead the series 52-31-4 all-time.
• Five of the last seven games have been decided by a touchdown or less.