If he didn't win a National Championship at a basketball power school like Arizona then why do you think he will win one at Texas?
At Arizona things were teed up for him to compete but he didn't even make it to a Final Four. Arizona had shoe $ NIL before NIL was legal and consistent Top 10 recruiting classes. (Miller was caught on an FBI wiretap discussing a $75,000 payment to the # 1 ranked recruit, who went to Zona and was the # 1 pick in the NBA draft.) The previous head coach had won a Natty and made four Final Fours in 24 years - Miller didn't make it to a FF in 12 years. Looks like his successor could be on track to make it this season, they were ranked # 1 much of the year. Most would consider Miller a very good coach but he hasn't yet shown he's elite.
I checked Miller's NCAA tourney record while he was at Zona. Call it 11 years since covid meant no tourney in 2020 - they made the NCAAs seven times (Lute Olson went 23 times in a row). Twice under Miller they outplayed their seeding - in 2011, his second year in Tucson they were seeded 5th but made it to the Elite 8, beating # 4 Texas and # 1 Duke. These were his only two wins against teams seeded higher. And in 2013 they were seeded 6 but went to the Sweet 16 by beating the # 11 and # 14 seeds.
Another year (2015) they played to seed, seeded # 2 and losing to # 1 seed Wisconsin by 7. No shame in that.
Four times they didn't play to their seeded level. In 2014 they lost to # 2 Wisconsin as a # 1 seed in the Elite 8 in OT. No shame there either. But his last three NCAA appearances at Arizona were really disappointing, losing early to # 11 as a 6 seed by 11 points in the Round of 64, losing a close one to # 11 as a # 2 seed in the Sweet 16 and getting blown out 89-68 by the # 13 seed as a # 4 seed.
He also had Arizona in the NIT one year as a 1 seed but they lost to 8 seed Bucknell by 11 points.
He's a good coach - good teacher and good recruiter - but he still has to prove he can take teams deep in the tournament.