The first time Cauldron says "hurt these people for a 2% greater chance of defeating Scion", and Apeiron says 'no', they might change their mind and decide they want to do it after all. The fact that they don't do this to regular capes doesn't mean they won't do it as long as the magic words "for the greater good" and "increased chance of defeating Scion" come up. And those come up for OP characters like Apeiron and most SIs a lot more often than they do for regular capes.
Except the entire problem, canonically, is they have no idea how to defeat Scion. At all. And have no way of gauging chances against him. At all.
At all, as in, PtV et al do nothing. Until Dinah, there was nothing. Even Dinah can't see
Scion's defeat - she only gets a hazy idea of how many people are alive afterward.
So since they don't know what to do, they focus on what they can do - they minimize societal collapse (and to be clear this is from text
and WoG, whether people want to accept it is a different conversation) and they try to keep high-powered capes alive but out-of-play with junk like the Birdcage.
And they pray that somebody shows up with a power that changes the game - naturally or by vial - before it's too late.
Cauldron is a lot of things, but I've never seen a good argument that they're dumb. I've seen plenty that
require them to be dumb because the alternative is Cauldron being right about things that the would-be argumentator can't accept, or because they just plain want them to get kicked in the face. But from an objective point of view, they shouldn't have got this far and managed this much if they're dumb. So assuming they're dumb is just bias out the ass.
So, back to Dinah. Now they can
finally get a number like "2% more billions of people survive if Apeiron shoots up a hospital." Because remember, can't see Scion himself even still.
On one hand, I can see them wanting him to do it, yes. Because arguments about the evils of utilitarianism get kind of weak when someone literally tells you, as a nigh-certain fact, 2 trillion people will die if you don't kill the 50 in front of you. That's why after they learned about Jack and Scion, they said "fine" - because the numbers said
everything would be even worse if they postponed Golden Morning.
But. Even if they decide they're willing to force Apeiron in principle, they then have to ask if they can, would it stick, and what's the risk. And the numbers on
that - courtesy of Number Man or the like, I imagine - are going to be absolutely 100% "don't do it."
Because they're not dumb, because a dumb Cauldron doesn't make a good story if nothing else. A smart Cauldron doesn't announce. Contessa asks for a path to persuading Apeiron through oration to do it that won't leave him hostile. If there isn't one - and I'm assuming PtV is bad at this because they don't use it as a sledgehammer for social like this afaik - then they use cutouts.
They path, say, Cherish into BB. Her engagement with Apeiron is inevitable. She can't help it. Even if she loses, Cauldron loses nothing. If she wins, Cauldron wins - because Cherish lives here too, she can't let Scion destroy Earth.
If Cherish fails, they point a battalion of Thinkers at the data and learn he's resistant to Masters, even if they don't know why.
Sooner or later, they conclude: 2% increased survivors if Apeiron shoots up the hospital. But any method of
forcing him to do it ultimately reduces chances. Or it doesn't, I suppose, in which case - depending on your interpretation of Cauldron - they try to force him, because even if he breaks free and fucks them up they just increased the chances of survival. Self-sacrifice, if you will.
But I think it's moot, because I don't actually believe there's a scenario where hamfistedly trying to mind control Apeiron materially increases survivors.
...If there is, that honestly says more about Apeiron's hangups than it does about Cauldron.