Sutter's opinion, which was supported by Treliving at the time, was the C doesn't matter, it's the leadership group that is important. After Gio left, there was no Gio/Iginla persona to fill the void, and it's more important that a core group matures together. He was trying to avoid having one player take on the burden of being the C in a hockey-obsessed city. But if you go by the conspiracy theory, he didn't name a captain because without a captain, the players had no way to speak to the coach, and thus were more easily manipulated and abused.
But I also think there were two other issues that transpired with the "C doesn't matter" mindset. I agree that the C doesn't completely matter and it's the group. But I think when certain other attributes were added on, it created its own distraction.
Sutter year 1 I think they hinted at a potential captain. We know Chucky really wanted it, but they didn't want to just hand it to him or have it contractually stipulated either which IMO is fair.
Year 2 though, again there were hints at a potential captain at the beginning of the season, but it didn't happen. Conspiracy theory wise, I think there's some truth in that perhaps Sutter didn't want someone to wield enough power to argue with him or maybe if the shouting matches rumors are accurate, it was also intended as some type of misguided punishment. But I also think that this facet annoyed and upset the players too by becoming an off ice distraction by causing the players to develop ennui very rapidly.
I think it's also worth noting that Treliving really didn't agree with what Sutter was doing, but technically let him do his thing. Rightfully or wrongfully, Treliving did indeed give his coaches a lot of power from Hartley, Gulutzan etc. I know that sometimes we think he should have intervened as GM or forced the hand by moving certain players (on occasion), but I'm honestly unsure how often a GM and POHO override coaches like that.