Yeah, people not in the war were happy, and those who came out wanted to be, but some just couldn't be.
Cassie and Jake's relationship was formed during the tension of fighting, and without that, it just fell apart. In real life, relationships based on surviving horrible events hardly ever last, despite what Hollywood tells you.
Tobias had no one. No real family, no real friends. Jake and Tobias respected each other, but were not necessarily friends. Same deal with Marco, but farther apart. Cassie and Tobias were never really close, and Ax isn't human (although still a good friend). Then there was Rachel, the only human he was trusting with and was truly close to, and then she was torn from him. As Jake's initial goal was to free Tom, Tobias' evolved to live peacefully near Rachel, although it wasn't stated outright. When that one person, one dream, was torn from him, he collapsed, and that makes sense.
Jake was just your average kid, but forced to make horrible choices, but as much as he hated them, those choices made him who he was. Without the war, he was nothing, is nothing. Without the fight, he wasn't himself. His persona is based on leading through a war, he grew up that way. Without it, he's just a shell, which lead to how he ended up, but that's also why he was secretly excited for the space mission in the end. In reality, he was just as dependant on fighting as Rachel, just more controlled.
Rachel was thoroughly and fully dependant on war. She needed the fight, it literally was who she was. After seeing that darker side of herself, that bloodlust, she simply would not be capable of returning to normal society. She knew this. Even if Jake hadn't told her to do that mission, she would've done something suicidal on her own. It only makes sense she would die with the war, because without the war, she was nothing.
Marco... he's just cold, utilitarian logic with a funny mask. He always knew what had to be done and knew he had to do it. He knew ending 15 lives to save 50,000 is what needs to be done, despite how wrong it feels. The funny mask aspect, however, is what saw him through. He always claimed to hate the war, but that's not entirely true. He's a master strategist, that simple. He doesn't need the combat and blood, but he knows he breaks down if he has to lead the simple life, after feeling that part of him. That's why he lives successfully after the war, but is immensely bored and empty, and why he agrees to go with Jake and Tobias.
Cassie truly hated every aspect of the war. She wanted no part of it, but only fought to protect what she loved and to try to stop evil. Her main conflict was the feeling of hypocrisy; killing to stop killers, subjecting others to what she wants to escape, etc. After the war, she no longer had to worry about that, and is the only one who is truly happy with the peace. She lives as a vet and communicator with other species, it's exactly what she wanted from the start without lying to herself. That's why Jake doesn't have her go along. He knows, while she's a key member of the team, she is truly happy now, and doesn't want to make her suffer for him. He knows another fight would bring them together, but its not worth it to him to see her sad again.
Ax was lost. He wouldn't die during the fight, there was no real reason for him to do so. He was an enigma, however because he had no people. He was an Andalite by blood, but he became who he was through humans, but he is not human. His actions would have definitely given him prestige amongst his people, but he would feel empty doing so without the Animorphs, which is one reason why he careless risks his life without second thought to board the suspicious ship, and why his final word was "Jake". It's only sensible that the enigma character has an indeterminable fate.