I think this suggests winning it doesn't have much impact on a team, good or bad. I'd say all of those NCAA tournament results are within reason of what you'd expect from each team given the regular season.Last year KU won the conference championship and then went on to win the whole thing.
2021: Texas, won first round, lost second round to #3 seed Purdue
2020: covid
2019: ISU, lost first round to Ohio State
2018: KU, final four run
2017: ISU, lost second round to Purdue
In fact, I'd say getting bounced in the semis in 2021 didn't hurt NC Baylor, or getting bounced in their first game in 2019 didn't hurt TTUs run to the NC game.
Not to mention ISU got freaking smoked by TTU in KC last year and went to the Sweet 16.
So the more I look at it the "successes" of the Big 12 tournament momentum are teams making runs that were in line with their regular season success. I see a lot more cases of teams bowing out early and having it not negatively impact their NCAA tourney. In other words, I don't think there is significant positive momentum gained by winning the Big 12 tournament.
If you can win it and bump up a seed or two, especially in a case where it might get ISU a Des Moines game, then it's pretty important. But as to indicating an over- or under-performance vs. the regular season due to momentum, it seems like that is not the case.