Currently thinking about how the death of Polites fractured the dynamic of the crew which led to quite literally the rest of the Odyssey in EPIC the musical. The entire crew relied on this man and NO, I am not exaggerating.
Polites served as the temperance of Ody; the diplomatic and optimistic council who was a liaison between the captain and his crew. Why? Well, Polites is never acknowledged to hold any power in the crew (we're talking EPIC canon here) but is clearly respected and valued by the captain. This combination is familiar; the crew is comfortable approaching Polites because he's their equal and Polites is comfortable approaching Odysseus with their problems because they're friends. That is his role.
Now I have my own issues with Eurylochus but I do think he's written well. And I also do not think he is fully in the wrong. HOT TAKE I KNOW, but hear me out: Eury was Ody's right hand. Odysseus is clever but he's also pretty humble (excluding the whole "I am the infamous Odysseus" but Bro had a right to crash out there). Odysseus does not surround himself with "yes-men", he surrounds himself with friends who are willing to challenge him. Case and point; Eurylochus and Polites.
Polites challenges his morals and instincts - Polites is always trying to ensure that Odysseus is doing what is best for himself. "You can relax my friend" is not something you tell your leader to do casually. It's what you tell your friend to do when they're working themselves too damn hard. "Greet the world with open arms" is not what you tell your commanding officer who you're trusting to get you home.
Eurylochus challenges his decisions. Always does, in every scene and NO that is not a flaw. He serves as a point of resistance so that Odysseus is forced to consider every option carefully. He makes sure Ody has considered the worst-case scenario and is fully prepared to back him up when that happens. Bro was ready to burn the Lotus island down if his friends didn't come back. Eury is the guy who's willing to strike first and make the difficult decisions, much like Ody is. He is a good second in command.
The point is: the two filled massively different roles in the crew. Eury is supposed to challenge Odysseus and question his decisions - that is his job; to make sure that his captain is making the best decisions for the crew. Polites is supposed to support Ody; he is a friend, a confident, and a source of trust and camaraderie.
What makes them such a well-oiled machine is that they all have specific roles and they are good at them. Ody makes the plans and decides what battles to fight, Eurylochus takes initiative and counterbalances Polites optimism, Polites offers ethical and moral support while counterbalancing Eury's cynicism. That is why the crew works so well.
Odysseus has someone to rely on and someone to challenge him. The crew has someone to confide in and a second in command to consider their needs. They have a captain who listens to both. Eurylochus and Polites have each other to balance out and a captain who values their opinions.
It works. It's balanced. It's a powerful type of leadership.
Then Polites dies, and so does that balance.
Eurylochus finds himself having to fill two roles. He has to question his captain and calm the crew. He has to place complete trust in Odysseus as Polites did, but he can't. His and Ody's relationship has always been based on challenging one another to ensure that they're considering every angle. He has spent his entire life being critical of Odysseus' plans because he knows that's what he's supposed to do. He doesn't have blind faith, he's a realist - optimism and trust were Polites forte.
Odysseus finds himself without that support and line of connection to Polites. He grows disconnected from the crew because of it and flounders when it comes to dealing with Eurylochus.
This is seen clearly in the song: Luck Runs Out
Eury was not in the wrong for pointing out how fucking crazy it is to casually ask the Wind God for some help. Sure let's go knock on a god's door and ask for loose change; HELLO!? There are so many ways it could've gone wrong and it has always been Eury's job to point such flaws out. It's what he's always done - probably what he's done for Ody throughout the war.
But Odysseus? He just lost his best friend and his mentor. His entire support system is crumbling, so being challenged by the one person who he needs to have his back pushes him into a dangerous space as a leader.
On the one hand, he cannot afford to have Eury question his every move, especially since Polites isn't there to challenge him for Odysseus. Especially now that he doesn't have Polites instilling trust in the crew - he can't afford Eury's challenges to eroding what trust remains in his disheartened crew.
On the other, pushing Eurylochus away and demanding staunch obedience from him is so out of character for their relationship that all trust between Captain and SOC is suddenly up in the air.
That is why Eurylochus opens the windbag. Not because he wanted "treasure", but because the captain who demanded he "be devout" is not the captain he's followed all this time. The captain who sits awake for four days, eyes following every crewmember with a glimmer of distrust is not the Odysseus Eurylochus knows.
Eury knows Odysseus with Polites. If Polites had been alive, he would've been able to quell the crew's distrust because he would have had full trust in their captain. Odysseus would've been able to trust his crew because he could trust Polites. He cannot trust Eurylochus to have that same blind faith, because Eury doesn't have it; and the crew knows it.
Everything's changed since Polites
It's not a throwaway line; it's what the crew whispers to Eurylochus. He's different. He's changed. Odysseus is not the same. Maybe it is treasure. Maybe he's lying to us. How do we know? How do you know?
And Eurylochus doesn't know. He isn't certain. Odysseus is his friend and his captain; that's a difficult power dynamic to balance.
So Eury opens the windbag, because he doesn't trust Odysseus. It's a different sort of mistrust though - not one of constructive criticism from a friend, but earnest dangerous mistrust of your superior.
Eurylochus leads the mutiny, because that was always his role as Ody's right hand; to question and stand against what he felt was wrong. To speak for the crew as another leader.
But Eurylochus never wanted to be captain. He never wanted to betray his friend. He felt he had to - Yes, he was willing to leave crewmates behind in Circe's lair because he has always been willing to make those hard calls.
Odysseus? He so rarely does what Eurylochus wants to do because they are not the same person. Eury doesn't want Ody to be him (Eury has flaws, but ambition is not one of them. He recognizes he isn't a good leader hence he immediately falls back on Ody's judgment after the holy cow bit) - he wants Ody to listen to him and consider his insights. So for Odysseus to sacrifice six of their crewmates without a word to his friend - without consulting anyone - without leaving space for his right-hand man to question him... that is when Eurylochus loses faith in Odysseus. Because that is not his captain. He doesn't know who it is. But his captain would never.
Hypocritical? Yes. But also rather insightful.
And Odysseus? He loses the last pillar of support he has in the crew, not because Eurylochus changes - not even because he changes. He loses it all because it is doomed to fall apart without Polites. It was all doomed to fall apart when they lost their counterbalance.
It is not Ody's mercy or ruthlessness that kills them. It is not Eury's distrust. Both of those existed far before it all went to shit. It was Polites dying. It was the fact that the three of them were so well suited for leadership as long as it was the three of them.
It had to be the three of them.