KU has had more All Americans and Olympic basketball players than any other school. They are second all time in wins, have the most conference championships, and as many Final 4s as UCONN & Louisville combined. They also are the only school to win the World University Games. The Jayhawks were originally coached by the inventor of the game and play 2 miles from his gravesite and his original rules are in adjacent building. 30 miles from KU sits the College Basketball Hall of Fame where more former KU players and coaches are enshrined there than any other school. Adolph Rupp played at KU on 2 Helms Championship teams. Dean Smith played at KU on a national championship team and a runner-up squad the following year. Arguably the greatest player to ever play basketball - Wilt Chamberain - donned the Jayhawk uniform in college. KU plays in a basketball arena that is always at the top of lists on greatest arenas in college basketball.
I think KU is among those schools (UNC, Kentucky and possibly UCLA) that ARE college basketball history.