I suspect it's going to turn out to be the case that Edward intends there to "not be enough stamps for everyone", ie, he wants to ensure there is at least 1-2 guaranteed failures. So even though there is the guise of "you're
totally allowed to work together" he actually wants division and conflict. That would serve the his purposes in at least two ways: first in cultivating the kind of Shadows they want (no big friendly organization, lots of self interested power grubbers who in turn will never form organized opposition or think twice about evil policies), and second in helping reveal any plots by Kate. After all, normal debutantes up to now always went in pretty blind with quite strict adherence to rules, and the normal brainwashing cultivated a certain amount of apathy towards others. Lots of wheels within wheels here.
I'll be interested to see if they all make it anyway, or if alternatively maybe Kate has fallback plans for failure, with Ram as an example. "Failures" get "disposed of" by brainwashing of the humans and if the Shadow is still alive it getting worked to death for soot. But like other parts of the adult system there is the potential flaw of them being so overconfident in their dependence on mind control magic that they have holes in their oversight. "Faceless Dolls" go everywhere without a second look, they're just considered part of the background unless some specific task is needed. So Kate might be able to use that to free a failed shadow/child and the adults will simply assume the shadow dissipated into nothing and the child has been converted to a faceless doll.
Could it be the case that controlling the soot sacks can be done by anyone?
I don't think
anyone can do it, but maybe anyone with the right kind of power can create them or something similar. A power like Evelyn's that can interfere with soot might also be able to seize control of one?
Anyway man is this going to be one heck of an arc.