Now that I've rewatched the episode a few times, I've decided that I don't have the energy to delve into the team's drama. Everyone at the Lighthouse or Zephyr has good intentions on top of selfish intentions on top of good justifications on top of bad justifications. Look at every one of 'em: if you view the situation from their side, you can understand why they are doing what they are doing, but if you look at one character from another characters POV and you can see they are making horrible decisions or even possibly being a downright asshole in some way.
Here's how I currently see it. Tell me if you think I'm wrong with any of these parts. These are not listed in any particular order but the characters are listed alphabetically.
I believe that this is an excellent analysis. I agree with nearly all of it and have at most quibbles with the rest.
I believe that nobody wants anyone to die, but you did a good job at identifying the people that each character is most concerned about. I am more confident than you are that nobody
wants Coulson to die or will want him to do so. The differences are mostly how far they are willing to go to prevent his death ranging from May and Daisy, who will do almost anything to save him, to Elena, who is the most worried about the negative effects of trying.
You can also add for probably everyone, "Doesn't Want: The world to become enslaved," although that may be implied in not wanting the world to be destroyed.
I am not sure what you mean by Coulson not wanting the team to do their job.
I agree that he does not
want to die. He is not suicidal. He only seems that way because he sees himself as being expendable due to a short life expectancy. He has made peace with this, but it is a shallow peace. He may fear that attempts to save him will just give him, and the team, false hopes of his survival that will be devastating when they fall through.
You can probably add:
Wants: Someone other than the team to believe him that the team saw the future.
Doesn't Want: The team to have any false hopes about his survival.
Doesn't Want: To go through a procedure as excruciating as the one he went through in the Guest House.
Doesn't Want: An outfit like the one that Talbot is currently wearing, even if Coulson thinks that it is cool.
She definitely does not want this position to become vacant due to Coulson's death. If Coulson does die, I suspect that she is ambivalent about taking over. I think she wants to please Coulson, but she does not feel up to the job.
He seemed to like the stuff.
At one time, she did not want any of the special features for her artificial arms that Coulson has on his arm. I do not know if that is still the case.
Fitz is the toughest. You can probably to two separate lists: one for Fitz and one for the Doctor. For example, Fitz may want to get the Doctor out of his head. The Doctor may want Fitz out. Fitz definitely wants Simmons to survive. The Doctor may be biding his time until he gets the opportunity to avenge his father. There may be a lot going on that we have not seen yet.
For Fitz, you might be able to add:
Wants: To be worthy of Simmons.
Doesn't Want: Deke to call him "Gramps" again.
At some time in the future, he will not want to design the time machine, and he really will not want to hear about Simmons's death ("There's so much blood.").
While not fully consistent, May seems to want Daisy to succeed Coulson if and when the time comes.
By "Doesn't Want: The team to fight," I assume that you mean "Doesn't Want: The team to fight with each other."
While there has been a fair amount of denial over the past few episodes, I suspect that Simmons still does not want Fitz to be the Doctor.