Alright, gents. I pulled some data for you all to consider. Here are all the national champions since the field expanded to 64 teams. Here's where the teams were ranked in the Final AP Poll, just days before each of the respective tournaments.
1985- Villanova, UR
1986- Louisville, #7
1987- Indiana, #3
1988- Kansas, UR
1989- Michigan, #10
1990- UNLV, #2
1991- Duke, #6
1992- Duke, #1
1993- UNC, #4
1994- Arkansas, #2
1995- UCLA, #1
1996- Kentucky, #2
1997- Arizona, #15
1998- Kentucky, #5
1999- UConn, #3
2000- Michigan State, #2
2001- Duke, #1
2002- Maryland, #4
2003- Syracuse, #13
2004- UConn, #7
2005- UNC, #2
2006- Florida, #11
2007- Florida, #3
2008- Kansas- #4 (#1 in KenPom, pre-tournament)
2009- UNC, #2
2010- Duke, #3
2011- UConn, #9
2012- Kentucky, #1
2013- Louisville, #2
2014- UConn, #18
2015- Duke, #4
2016- Villanova, #6
2017- UNC, #6
2018- Villanova, #2
2019- Virginia, #2
2021- Baylor, #3
2022- Kansas, #3
2023- UConn, #10
Here's the count by rank:
#1- 4
#2- 9
#3- 6
------------
#4- 4
#5-10: 9
#11-25: 4
UR: 2
38 NCAA Tournaments and exactly half of the national champions have been one of the top 3 teams in the Final AP Poll. I feel confident that UConn and Purdue will stay in the top 3. The #3 team is still up for grabs. If Houston is the third best team, I kind of like my odds, mostly because it feels like there's a decent gap between UConn/Purdue and everyone else.