"Our job is to correct history gone awry," I told her. "The form that takes isn't always going to be pretty or palatable."
You're probably aware, but the job of Chaldea isn't actually to restore history as it was.
That's more or less taken care of by the Corrective Force.
Rather, Chaldea can't really alter history all that much.
The rule enforced by the World is that actions of parties that don't qualify as "living humans of the era" cannot alter the era in any way that contradicts the explicitly defined contents of a Quantum Time-Lock, absent the caveat of installing a Grail the hard way like Goetia did — making use of agents who qualified as "living humans of the era."
Explicitly defined content isn't "all the history within this era." It's largely "the history that most every living human within the era observed / can agree upon."
This means that things aside from that can be changed without incurring the action of the Corrective Force — including killing or saving specific humans whose fates aren't specified by the QTL.
Comparatively, events explicitly defined by a QTL cannot be changed absent of the caveat named above. If changes are made to these events, the Corrective Force will act to revert them back to whatever the QTL defined.
The problem is, the Corrective Force can't do its job so long as a Grail is asserting an incorrect history across the entire spectrum of a Quantum Time-Lock, and the World / the Human Order doesn't have the ability to independently excise Grails.
Chaldea's job is really just to do what the World / the Human Order can't — to remove the Grails via rayshift.
Incidentally, rayshifting is largely restricted to predominantly spiritual existences such as human souls, Grails, and homunculi — and certain inanimate equipment modified by Chaldea in an unspecified manner. Other things, such as food and other provisions, can be transported, but this appears to be done via a special bag created by da Vinci.
Ergo, if there isn't a Chaldea-like group around to take care of the Grails, and there's someone who's actually interested in altering history — unlike Goetia, who only established his seven Singularities to dummy-content the Human Order with nonsense data — they can actually use Grails to thumb-tack history into a new shape.
Lostbelt 3 QSH planned to do so as a backup plan against the Alien God in the event that Chaldea got itself annihilated.
