So, ranking schools by Championships in the Near-Modern and Modern Era:
1) Duke - 5 - 1991, 1992, 2001, 2010, 2015
1) UNC - 5 - 1982, 1993, 2005, 2009, 2017
3) UConn - 4 - 1999, 2004, 2011, 2014
3) Kentucky - 4 - 1978, 1996, 1998, 2012
5) Kansas - 3 - 1988, 2008, 2022
5) Villanova - 3 - 1985, 2016, 2018
5) Indiana - 3 - 1976, 1981, 1987
5) Louisville - 3 - 1980, 1986, 2013
9) UCLA - 2 - 1975, 1995 (plus most of the championships from the "asterisk" era)
9) Florida - 2 - 2006, 2007
9) Michigan State - 1979, 2000
Those are the championships in the era of basketball that approximates the game played today, covering almost the last 50 years.
Rupp's championships and whoever was coaching Indiana in the 40's championships simply don't count. The game and the tournament were so different back then that it is apples and pumpkins to compare a championship in the early 50's to today.
That said, the first 8 schools on that list have 30 of the 48 championships during this era. They are definitely a class above over a long period of time.