So this'll be a controversial arc.
It's certainly a choice to swap to the antagonists' PoV right after emotionally devastating the protagonist. But I'd be more surprised if Ryouko had any intention of making the audience suddenly open our hearts to them. The decision to place a page of them laughing immediately after Satsuki's breakdown was extremely deliberate. These aren't people you're meant to like or justify. Nobody wants to sympathize with them, and Ryouko's smart enough to get that.
But their perspectives are important. Kai is the anti-Satsuki: willing to use underhanded methods to save lives by setting up death. He's driven, if not straight-up blinded, by a sense of righteousness potentially born from guilt like Satsuki's. He and Satsuki both struggle to understand each other; Kai still thinks he can convince Satsuki to see things his way as shown by him getting disheartened when Michiru's death hurt her more than expected. I think he is good deep down but completely warped into lawful evil.
And it's less obvious, but Sayoko is the anti-Akira. Child of a (probably) broken home, distrustful and abused to the point of hopelessness. It's implied now she's the one with darker tendencies. Even before meeting Kai she seems to have fixated on death as a solution. Rather than any noble purpose, she's in it for attachment to Kai. But they might have their own disagreements on who deserves justice. Her whole standoff with Satsuki in chapter 39 seems like it'll be significant.
There's several points I'm looking to see this flashback cover:
If I'm speculating, Kai chose a nonviolent method and it backfired, scarring Sayoko. She pushed him to kill and the rest has been him proving he's capable of it. Looking forward, the truth behind Michiru could be what breaks them. Kai's righteousness can't handle killing innocents. But Sayoko's maybe different. I doubt she'd abandon him but that's where things start to crumble. And from there I wouldn't be shocked if they got undercut by a new villain. Like maybe Seo, since she's the only one who can expose the truth with Michiru.
I don't know if the student council will ever get redeemed and I don't think this is the kind of cliched flashback designed to do that. Rather than trying to get the audience to feel merciful, I think Ryouko's taking steps easing us on allowing someone to die. Most would agree with Satsuki that murder isn't a solution. But we're all going to have edge cases we might not admit until it's life or death. And the moment this manga gets you to cross that line, you are sympathizing with their perspective, just not them.
Their narrative purpose could easily be a cautionary tale against taking life into your own hands satisfying your own sense of justice. I feel like I obsess on this, but all signs point to how Satsuki will ultimately handle Akira and her father. It's a direct reflection of Kai saving Sayoko from her abuse, and they'll try to tempt Akira and Satsuki down the same path.
Frankly I really want that to be Satsuki's moment to tell them to fuck off and prove she can do it her way. When she's ready to come back, it's not like she'll be in any mood to pity them either.