Dealing with young people in this situation presents a couple of problems. One is time - how much available time does a coach have to spend with an individual player that needs special treatment when they have an entire team that needs their attention? The other problem is favoritism, real or as percieved by teammates. Can a coach yell at one player to get their ass in gear and then politely ask the next to please try harder to get in the correct defensive position?
Everyone knows who Auriemma is and everyone knows his coaching methods. A recruit coming to UConn should expect that the coaching staff is going to demand their absolute best effort. His coaching methods have won a lot of basketball games and even a few awards. How much should he have to change how he coaches to accommodate a player? What guarantee is there that a different approach would have a different effect?
I honestly don't think that time is an issue here. Given the relatively small size of a basketball roster, the number of coaches, and the remarkable amount of time they spend together, I don't think anybody is short-changed on time. Favoritism can be an issue - when you read some of the books about the program, and read about some of the upperclassman/underclassman conflicts, some of the nicknames ("precious"), and just the human nature of competative people, there's gonna be some perceived inequities. Perhaps, even some real ones.
Geno has mentioned, many times, how he has had to change his coaching methods through the years. Some of his players from the earlier years are on record, commenting about "how soft he's gotten". I think what you're asking is, where's the line between trying a softer approach, and coddling a player? I don't think anyone can answer that, because it's not a hard-and-fast demarcation. I can think of a couple of ways to explain it, but they're kinda simplistic. One is "you don't have to sit in the same pew, but ya gotta be in the same church", which is to say, your value set and objective have to be the same, but you don't have to take the exact same path to get there. Another is to note that the song "Stardust" has been recorded, I believe, over a 1,000 times. Imagine - over a thousand different renditions of the same song - same lyric, same melody, but different pacing, emphasis, feeling.
I'm reading "Francona: the Red Sox years" right now, and it's pertinent to this topic. Terry Francona, in his first year with the Sox, had to manage Manny, Pedro, Nomar, Millar, Lowe, Buckholtz, Damon, Ortiz, etc.. - the "Gang of Idiots". And, he had to deal with the issues mentioned above - jealousy, perceived favoritism, finding which buttons to push with which players. With grown men, professionals, not 18 and 19 year-old students, the issues were, and are, the same. In short, I don't think there's a nice, clean, black-and-white answer. You need a patient, gifted, experienced coaching staff to make the calls as they best see them, and hope they're right.