UConn has as much of a claim as Indiana or more of one IMO. Indiana hasn't won it all in 31 years, UCLA has all the history but hasn't won it in 23 years. Kentucky, Duke, UNC, and Kansas are the only consistently great programs who also win titles.
UCLA has the most titles, a top 5 win%, tied for 2nd most FF, and 2 final fours in the last 11 years.
Blue blood is about history, so don't think you can dismiss that out of hand. Lineage. Bloodline. You need continued current success, sure, but UCLA's final fours being within a decade are good enough for me considering the overwhelming history.
Teams with 15 or more Final Fours is a pretty easy cutoff. UNC, Kentucky, UCLA, Duke, and Kansas. All between 15-20 FF. Next highest is 10 FF. All 5 of those schools wear blue. Easy, done.