I'm obviously biased, but I'm with the OP, for one reason in particular: UConn basketball is not, and has never been, dominant on the recruiting trail. To me, the fact that we've won four championships in the last 16 years, with - save for a couple notable hold-overs on the last team - four entirely different rosters is much more impressive than professional sports teams winning with the same players every year. Of course the Patriots have had a dominant run, Tom Brady is one of the best quarterbacks of all-time. Of course the Spurs have had a dominant run, Tim Duncan is one of the best basketball players ever. You get the point. In football, Alabama has dominated, sure, but they have the luxury of trotting out more four and five star talent on their practice squad than 99% of D-1 programs have on their whole roster.
Of course, UConn doesn't recruit nobodies, they've signed quite a few four and five star players themselves. But in comparison to other elite programs - Kansas, Kentucky, Duke, UNC, etc. - the contrast in McDonald's all-American talent is jarring. UConn is the best program in the country at identifying, developing, and maximizing talent, and there isn't a close second.
