OK....so lots of data below, but it looks like BYU has knelt to end the game 28 times (14 in scoring position*, 14 outside of scoring position), and has had 3 opportunities to kneel out the game that they didn't (as best I can tell from looking at game logs and YouTube videos of games).  I also highlighted the times in that span when opponents ran out the clock instead of scoring on BYU and those times when opponents opted to keep running plays rather than kneel to end the game.

Big takeaway for me is that we haven't been hurt by an unwillingness to run up the score.  Of the 14 games we were in scoring position, they were almost all against very bad teams (UMass, Idaho St, UNLV, McNeese St, Portland St etc) and with huge leads.  Beating UMass 55-3 or 58-3 doesn't really make a difference in how BYU will be perceived.  The only exceptions were

• against Virginia 2021 (still a 3+ possession lead, but a quality opponent, so maybe would have helped to beat them by more)
• UNLV 2017 and Portland St 2017 (terrible opponents, but only a 2 possession lead, so maybe would have helped to beat them by more)
• Washington St 2021 

That last one is also the right choice as it was a 2 point game.  Kicking a long FG or otherwise trying to advance the ball might have given Wazzu an opportunity to pull a late miracle.

*for purposes of this, I designated as being close enough for 50 yard FG (or less) as in scoring position

All data is below

No opportunity to kneel the ball

1. Arizona St 2021 ended with ASU in possession
2. Boise St 2021 ended with Boise St kneeling the ball (outside scoring range)
3. Baylor 2021 ended with Baylor kneeling the ball after a late BYU TD made the game look closer
4. UAB 2021 ended with UAB kneeling the ball in short FG range
5. Houston 2020 ended with Houston in possession (BYU scored late instead of kneeling, but couldn't quite have run clock out)
6. Texas St 2020 ended with Texas St in possession
7. North Alabama 2020 ended with N Alabama in possession after late BYU TD (couldn't have quite run clock out by kneeling)
8. Coastal Carolina 2020 ended with BYU driving to try to win game and running out of time
9. Utah 2019 ended with Utah kneeling the ball at BYU 4
10. Tennessee 2019 went into overtime
11. USC 2019 went into overtime
12. Washington 2019 ended with Washington kneeling the ball in medium FG range
13. Toledo 2019 ended with BYU driving to try to win game and running out of time
14. USF 2019 ended with BYU driving to try to win game and running out of both time/downs
15. SDSU 2019 ended with SDSU kneeling ball after missed BYU FG
16. Hawaii 2019 ended with Hawaii kneeling the ball after BYU interception
17. Arizona 2018 ended with BYU running out the clock but needing to run plays to do so
18. Cal 2018 ended with Cal kneeling the ball just outside FG range (interestingly, BYU called a timeout to force the kneeldown)
19. Washington 2018 ended with Washington kneeling after BYU scored to make it 35-7
20. USU 2018 ended with USU kneeling outside FG range after failed BYU onside kick
21. Northern Illinois 2018 ended with N Illinois quasi-kneeling (making moves running backward to burn extra time, but not trying to advance the ball)
22. Boise St 2018 ended with BYU driving to try to win the game and running out of time
23. Utah 2018 ended with Utah kneeling ball (outside scoring position) after BYU turnover on downs 
24. LSU 2017 ended with LSU opting to NOT kneel the ball and running plays (near midfield) to run clock out
25. Utah 2017 ended with Utah kneeling ball in redzone after BYU turnover on downs
26. Wisconsin 2017 ended with Wisconsin opting to NOT kneel the ball and running plays (in redzone) to run clock out
27. Utah St 2017 ended with USU quasi-kneeling (using extra moves to run a bit more time, but not trying to advance the ball)
28. Boise St 2017 ended with Boise St kneeling the ball while in medium FG range
29. Mississippi St 2017 ended with Miss St choosing to NOT kneel the ball (near midfield) and continuing to run up the middle
30. Eastern Carolina 2017 ended with ECU kneeling near midfield
31. Fresno St 2017 ended with Fresno St running clock out (no opportunity to kneel) at BYU 4
32. UMass 2017 ended with UMass kneeling near midfield after failed BYU onside kick
33. Hawaii 2017 ended with BYU needing to run plays to get 1st and allow clock to run out

Not in scoring position, kneeled out the game

1. Arizona 2021 after recovering onside kick, not anywhere close to scoring position
2. Utah 2021 after Utah turnover on downs, just outside of FG range
3. Utah St 2021 after USU interception, right at the extreme edge of FG range (51 yards)
4. Idaho St 2021 after Idaho St turnover, at BYU 4 yard line
5. USC 2021 after USC turnover on downs, inside BYU 10
6. LaTech 2020 after LaTech interception, on BYU side of field
7. UTSA 2020 after roughing the punter call kept drive alive, near midfield
8. SDSU 2020 after SDSU fumble, on BYU 20 
9. Boise St 2019, on BYU side of field
10. Liberty 2019 after Liberty turnover on downs, outside FG range
11. Wisconsin 2018 after Wisconsin missed FG, on BYU side of field
12. New Mexico St 2018 after NMSU punt, at BYU 11 (worth noting that BYU appears to have gone for it on 4th and 2 with less than 2 minutes in this game with a 35 point lead...)
13. Western Michigan 2018 after BYU drive, near midfield 
14. San Jose St 2017 after SJSU touchdown, at BYU 10

In scoring position, kneeled to end the game

1. Wash St 2021 with 2 point lead, BYU knelt while in long FG range
2. Virginia 2021 with 3+ possession lead, BYU knelt while in medium FG range
3. GaSouthern 2021 with 3+ possession lead, knelt while in red zone
4. Navy 2020 with 3+ possession lead, knelt while in red zone
5. Troy 2020 with 3+ possession lead, knelt while in red zone
6. UCF 2020 with 3+ possession lead, knelt at UCF 4
7. USU 2019 with 3+ possession lead, knelt in redzone after 73 yard interception return
8. Idaho St 2019 with 3+ possession lead, knelt at Idaho St 1 after long drive
9. UMass 2019 with 3+ possession lead, knelt in red zone
10. McNeese St 2019 with 3+ possession lead, knelt at McNeese St 4 after McNeese St fumble
11. Hawaii 2018 with 3+ possession lead, knelt in red zone
12. UMass 2018 with 3+ possession lead, knelt in medium FG range
13. Portland State 2017 with 2 possession lead, knelt in medium FG range after Portland St turnover on downs
14. UNLV 2017 with 2 possession lead, BYU knelt at UNLV 3 after long interception return

DIDN'T kneel the ball and kept running plays from scrimmage (to run clock out)

1. USF 2021, BYU was actually in scoring possession and DIDN'T kneel - including after a fumble which BYU luckily recovered
2. Boise St 2020, kept running plays from near midfield

DIDN'T kneel the ball and kept running plays from scrimmage (to score)

1. Western Kentucky 2020, could have knelt but instead continued drive, kicking FG.  Game then ended with WKU in possession