I also disagree. Given the amount of time and effort a coach must put in, there is no way that he can never have a vested interest. They inevitably and understandably develop friends, favorite, and foes. And once students have ceded power to that administrator or coach, it is VERY difficult to recapture.
I can speak on this having been in both positions now. I started out as the captain of a team in a program without much in the way of attorney coaches. Our educational coach would set the rosters, but a lot was left to the students and if we lost students we usually did the recruiting to replace them and made the personnel decisions on our own team.
When I graduated, we shifted to a hybrid student/coach program that vests complete competitive authority in the coaches during the year. The first year was more difficult for me as head coach because I was trying to run a program whose leaders were all people I competed with, but we also had only 8 people returning (down to six eventually), so the "favorites" were the people we needed to lead anyways.
We won't be totally free of people I competed with until next year, but all it took was one year of coaching for the ties of competing to be completely eroded away. It was really tough to make some of the decisions I had to make, because of those ties, but not as tough as it would've been if I were a student.
Maybe it's because the coaches vote on things as a group, but I think we didn't ever let any personal biases get in the way. We always did what we thought was in the best interests of the program, and any personal biases we did have would be counterbalanced by the fact that our 7 coaches (6 after Z left to return to Arizona) would all be inclined to have different favorites and goats which would cancel each other out.
Prior to that, we had 1 coach, but mostly the program ran itself, and there was a lot more petty infighting, duplicity, and favoritism in the old system than there is now. I've really got to agree with Jimmy, but trailered with this one caveat: Every program is different, and what works for one program won't work for another. If student run works for you guys, more power to you. If our program had been entirely student run last year, I really think some of our mockers would have been capable of taking the life of their fellow students.