the majority of Division 1 basketball schools or FBS/FCS football schools participate. Zero.

There are 364 schools that play division 1 basketball and 263 FBS/FCS football schools.

Utah claims NCAA National Championships in 3 sports: Skiing, Women's Gymnastics, and Men's Basketball (1944).

Only a handful of schools compete in skiing. Like a dozen. And some of those only compete in select events.

There are only 62 schools that compete in Division 1 Women's Gymnastics.

In 1944, many schools didn't field a basketball team (WWII), and the NIT was at least as prestigious--moreso in the eyes of many contemporary sources. In any event, a split title is an accurate description for a Utah team that was bounced in the first round of the NIT before being a late addition to the NCAA Tournament when Arkansas couldn't field a team. Summary: Split title rather than concensus.

Just kind of an oddity that Utah doesn't have a single consensus National Championship in a sport where the majority of major college athletic programs field a team.

BYU, on the other hand, has 11 consensus National Championships in sports where the majority of major programs participate:

1970 Track and Field (more than 275 schools)
1981 Men's Golf (more than 275 schools)
1984 Football (263 FBS and FCS football programs)
1997 Women's Cross Country (more than 340 schools)
1999 Women's Cross Country
2001 Women's Cross Country
2002 Women's Cross Country
2019 Men's Cross Country (more than 310 schools)
2020 Women's Cross Country
2024 Men's Cross Country
2024 Women's Cross Country

BYU also has championships in sports with lower number's of schools participing (such as Men's Volleyball).