More than wins, Kansas has history. 6 years after inventing the game of basketball, James Naismith moved from Springfield to Kansas to work at the University of Kansas. Basketball was played in YMCAs and by women before then, not at universities. So Kansas was the first university at which basketball was played. It was really at KU that the modern game of basketball was developed, including many of the rules -- for example, there was no dribbling until Naismith went to Kansas.
Phog Allen, who succeeded Naismith as coach at Kansas, was not only a famed coach but also an evangelist for the game who got basketball accepted as an Olympic sport and served as US Olympic team coach.
By comparison, UCLA is a flash in the pan, it was successfully only for a short period under John Wooden, a success tainted by payments to players. Similarly with Duke, largely a one-coach school, and we'll probably find that they've been paying players.
If there are any blue bloods in college basketball, Kansas is one.