Following UConn for a number of years may lead someone to believe that it's easy to find a coach that can win a national title but it really isn't all that easy.
NC State was a great brand with a long history coming off two consecutive head coaches that had won national titles yet hasn't been able to get back there in a little more than three decades.
Indiana was as big a name/brand as there was in college hoops. Davis ws able to take Knight's recruits to the title game year one and that program, after bringing in guys with impeccable track records more than once continue to fall.
Ohio St has been trying for six decades. UCLA (with a couple minor exceptions) for nearly three decades (and save that one Harrick year, five decades).
Look where Georgetown is today compared to the Hoya Paranoia years. Look at DePaul post Ray Meyer. Louisville has fallen off a cliff. Florida (albeit, with less history) has proven they cannot win it all without Donovan. just as Arizona has proven the same without Olsen.
Peronally I would not be willing to make a substantial wager on the likelyhood of Duke or UNC winning a national title with their current head coaches and I also would not be willing to wager even a small amount that Michigan St or Kentucky would win another with their current head coaches.
Your claim was that the BE has schools that win national titles. If Jay Wright was still on the sideline you would be correct. He isn't and again, the one BE school that does qualify may be in the B-12 or ACC in six, eight, ten years.