Just clarifying, the starter for the '91 season and the '92 Orange Bowl was Keithen McCant, who was an above average passer. Joseph was the starter for most of the '90 season, and Grant was the starter for the beginning of the '92 season until Tommie took over. Mickey and Grant were NOT good passers. Tom Haase was decent, but we only saw him briefly against Georgia Tech in the '91 bowl game.
Also, just to quibble, Frost struggled to pass in slippery conditions, most likely because he has relatively small hands. If you watch the '96 Colorado game, the ball kept slipping out of his hand as he was passing.
Finally, you simply can't judge the passing of an option QB by the same standards as the passing of a team in pass-first and/or pocket passing offense. Option QBs get hit ... a lot. Getting hit makes it harder to pass. Tommie Frazier was recruited by almost every major college program to be a pocket passer, but HE wanted to be an option QB, which was why his final choices were Nebraska, Notre Dame, and Clemson. Miami wanted him to be a pocket passer. He would have been a good one. If he could stand in the pocket and just throw, so much of the struggles of passing as an option QB disappear. Ask anybody who ever played option QB how it hurt their passing, and they'll probably tell you war stories for as long as you'll listen. It especially hurts QBs who aren't good at using their elusiveness to avoid direct contact. Jamelle Holieway and Turner Gill were excellent at avoiding hard hits when running the option. Although they weren't/aren't option QBs, Taylor Martinez and Adrian Martinez were/are NOT good at avoiding unnecessary contact when running the ball. I don't ever want to see a Nebraska QB landing on his helmet, shoulder pad, or back EVER again. A smart running QB will do some version of Marcus Allen, who could twist and contort his body to avoid ever taking on a direct shot. The best ones not only fall forward, but find a way to twist while falling to go down as slowly as possible.
The same concept works against pocket passers, fwiw. Go back and watch Jojo's strip-sack on Haskins in the 2018 Ohio State game. He landed hard, and he never fully recovered in that game or the next. He had a hitch in his passing from that point all of the way through the 2nd half and through the Maryland game the following week. It hurts to throw with a sore shoulder, and it's natural to adjust your throwing motion to limit the pain,... which screws up your passing.