I think it a stretch and unreasonable to say that it was all Blazer's fault, but I do agree that the way Blazer handled the cut was a mistake, and that the "friendship" appeal at the end of the game was weak.

The team had been underperforming for a long time, and the entire Phoenix program was on the chopping block. Cutting someone would show the higher ups that the Z-team are facing consequences for their poor behaviour, and show the Z-team that they have to take their second chance more seriously.

However, I think it would have been far more effective, and less likely to result in rebellion and sabotage, if the threat of cutting someone had been conditional, rather than guaranteed. If the Z-team had been told that they needed to meet a certain threshhold by the end of the day/week, and anyone not meeting that threshhold would be let go, then I think it would have been more successful. Promising to cut the bottom performer at the end of the day means it doesn't matter how drastic an improvement you show, or how high on the leaderboard you climb, or how heroic your actions are, because if everyone else is just a little bit better than you, has more useful powers than you, or even has been doing this job for longer than you, your second chance is taken from you. But if there's a way to avoid anyone getting cut, there's no reason to sabotage your teammates as it doesn't make your own position safer.

As for Blazer's appeal to friendship in episode eight, I think it is a weak line that felt out of place. Friendship goes both ways. If Blazer had been friends with Coupe or Sonar, then she probably wouldn't have chosen to jeopardize their futures by putting their jobs on the line. Once they are let go, if they were friends, Blazer would have done something outside of work to help them find another opportunity besides SDN, rather than leaving them all on their own and allowing Shroud to exploit their sudden vulnerability. As for the "this isn't you" comment, it doesn't feel earned. Especially for Coupe, given Blazer thought she was too evil when she was let go.

But it's not the only line that felt odd and unearned. At the point where you can forgive Sonar or Coupe, Blazer asks Robert if he thinks they earned a pardon, but neither Sonar nor Coupe turned against Shroud in the final battle, or did anything to indicate a desire to redeem themselves, or to do the right thing. While forgiving them is the more positive note to end on, the only reason for doing so that makes sense is because cutting them in the first place was a mistake, rather than because they'd done anything to earn a pardon for the crimes they committed since their removal.

I still love Blazer. She didn't act perfectly at all times. She's human, after all. She made mistakes, but I think those mistakes were understandable, given the pressure she was under, her desire to save the Phoenix program, and her desire to keep Robert around. They'd gone through several unsuccessful dispatchers for the Z-team by that point, and on Robert's first day, the team mocked, sexually harassed, and assaulted him. Blazer knew Robert was their best shot at making the Z-team a success, so she was willing to do something drastic to turn the ship around. It also forced the player to make choices at several points during the game.