Soccer??? Not this year. (I don't follow, but both my schools, RU and Arizona, made the dance, both bowing out in the 2nd round).
Per Wikipedia UConn is around 47th in team championships, with 22; that's 2 positions ahead of Arizona's 21. UCLA, Stanford and USC all lead with over 100, then Penn State's 83.
Even just considering sports, in general, UConn is good, no doubt. But the "powerhouse" status is probably a bit away as an all sport school. Yes, better football would help.
It could be worse - I love Rutgers and they have enjoyed some modest athletic success in WBB, Women's Soccer and wrestling, in particular, but I will grant you that UConn is ahead. Arizona - over-all - has a well balanced athletic department. Successful in almost everything, sporadically very successful. Softball, Baseball both have Nattys, volleyball is usually in the NCAA's (not this year), women's soccer has been good of late, golf, swimming and gymnastics have all had good runs.