I kind of want to look this up tomorrow.. but I suspect a very high percentage of title teams had at least one first round draft pick, and I bet the same applies for final 4 teams (obviously you have wild runs like Loyola). I'm not saying you HAVE to have an NBA talented player on your roster, but it sure helps.
Baylor still had lottery pick Davion Mitchell. Uconn had Newton and Castle and Clingan. Houston has lottery pick Jarace Walker, Alabama has pistol-holding Brandon Miller. Virginia had DeAndre Hunter, their opponent Texas tech had lottery pick Jarret Culver..
Kentucky doesn't currently have a 1st round pick projected (tankathon doesnt even have us with a 2nd either) and i think if you want to win in March it really helps if you have that NBA-level talent that can just outperform most other teams opponents, or atleast a couple guys worthy of the 2nd round.