There are Helms Champions from before the tournaments, and the NIT and NCAA vied for prominence up until 1950, so Helms is still the best way to go until 1950.
Including the two KU championships from the 1920s explains the difference between KU and Connecticut.
KU championships: 1922, 1923, 1952, 1988, 2008, 2022
Conn championships: 1999, 2004, 2011, 2014
Duke championships: 1991, 1992, 2001, 2010, 2015
But part of Miami football is that they are not long-tenured - they are ranked in the mid-40s for total wins. Duke, on the other hand, is ranked #4 for wins.
So perhaps UConn IS Miami, whereas Duke is more of a Nebraska, who played for a long time with many wins, but only started winning championships post-70s.
And Kansas is Alabama or USC (but not ND, because they've actually won it all recently).