In your estimation, what in Kansas' profile makes them a P5 must-have, while UConn is stuck in the G5?
Market?
Academics?
Basketball success?
I don't think Kansas is taking a spot in lieu of UConn. It's more about Kansas overall. I'd say all of those things put together (market, AAU for academics, basketball history and prestige) are what makes Kansas attractive.
Let's put it this way: if you put Notre Dame's resume from the past 20 years into a pile of all FBS schools but removed its name (meaning that it has a blind resume), you might find a dozen or more schools on paper that would look more valuable than Notre Dame. Maybe those schools have more success on-the-field, larger markets, and even higher TV ratings over that time period. Yet, if you were to poll university presidents out there about who would be the most valuable football addition off the top of their heads without any data, they would almost universally say Notre Dame. You can't remove the name "Notre Dame" from the process.
Kansas has pretty close to that name brand status with respect to basketball - maybe not Notre Dame status (that would be Duke), but it's at the level of Michigan/Ohio State/Alabama as a football equivalent. They're not just a great program - they also have the extra qualitative oomph from the national brand name that has been built up through history that only a handful of other basketball programs have (meaning that they're going to be an elite school that sells tickets and drives TV ratings whether they're up or down in any given year). When you combine that with their AAU status and massive national fan base, it makes them an automatic invite to any other P5 conference.
And look - I know that Kansas would lose to UConn in a blind resume comparison from the past 20 years. Heck, I think UConn might actually beat EVERYONE on a blind men's basketball resume from the past 2 decades (and UConn would certainly beat everyone on a women's basketball resume in all of history). However, you just can't remove the names from the process. You don't need to sell the university presidents about the value of Kansas any more than they need to be sold about the value of Notre Dame: they just KNOW it already because of their historical pedigree.