See, this is the difference between someone who has been there and a fan. The true fast break is ran with actually play sets out of the defense. This is practiced based on opponent. Then you enter the secondary break, generally anywhere from 3-5 set plays that attempt to get what a fan would classify as a fast break basket that is, in fact, a set play. Most of the time this is based on the defense that has been set on the play that lead to fast break. Then you enter into your half court if neither the original push, nor the secondary pushed worked out. It is all planned in college, I would assume, much like most pro sports, it gets even more choreographed at the pros. The fact that you think it is counterproductive is because you haven't seen all designed out. Ex. Out of 55 (man D) we would transition into the break. 2 and 3 go wide, 4 comes down right side of bucket, 5 comes down middle; from there, if an easy layup/dunk doesn't present and depending on matchup defensively (aka who picked up ball and basket) 2 and 3 would come under the basket crossing, 2 would flair straight out baseline to 3 point area and 3 would hit a 45 degree angle between baseline and free throw line. Now, if our video sessions panned it out,or if we saw it in game, that they were switching on screens....if 2 was on 2 and 3 on 3 (basically if who we thought would guard specific players held true on that break) 2 or 3 would set a screen for the other to try and get the switch and create the mismatch. From there, a lot of things could happen, but almost exclusively based on film study for defenders tendencies. If you can't transition from your fast break to your secondary to your half court set, you will not win many games...unless you are attempting the entire Loyola Maramount things under Hank and Bo where you don't care about D nor plays, just scoring 140 and hoping you don't give up 150.
As for title teams, not many run it, Izzo runs a variation depending on the year and Syracuse ran it when they had powerful bigs, not so much when the were wing and guard oriented. Wisconsin has ran it at times when they went away from just playing big, but their version is heavy post oriented. It requires a smart team, very smart, which honestly is probably why you don't see many men's teams run it but you see 3 of the best programs in women's history do or did during their heydays...Stanford, Uconn (still runs it), and Tennessee under Pat Summit. Now that men's rules more closely mirror the pros (in terms of protecting the offense to drive scores up) that just occurred this year, you may see more running it. Teams like UK will never run any of it, its not a learn in one year offense, at least not to the level of winning titles and UK is a one and done type program for the most part. Teams like UW, Duke (who has it as part of the offense but has lacked the bigs for quite a while compared to what they used to have,) MSU run it or run sets out of it because they get enough upperclassmen.