We have it on some authority that a precognitive received a vision suggesting that the complete destruction of Mirror would result in devastation. Claude may be able to explain that in some greater detail. That said, whether or not we presume it to be truth, the warning is there. We do have both a piece of Mirror, and a tool with which to break her—however . . .
There are essentially two parts of Mirror—two personalities. The one that, by all rhyme and reason, you are right to want to destroy. But the other . . . perhaps, not so much. We are wondering if there is perhaps a route to take that would allow the one aspect of Mirror to be restored, and one to be destroyed.
Simply attempting to destroy Mirror . . . I feel like it would draw too much attention, and given the warning, potentially be too much of a risk without bringing us any benefit. Regarding how we might benefit; I am not fully suggesting that it is possible or even ideal to regard Mirror as an ally, but we may potentially be able to bargain with her, if we are able to figure out what it is she might want, and from that, we may be able to procure some measure of assistance towards our final goal.
Tangential to that, we may possibly be able to use Persona's power to separate the two aspects of Mirror and destroy that which needs to be destroyed, while preserving the rest—allowing for multiple standpoints to be satisfied.
There is also the question, of course, of if or when the final pieces should be returned to Mirror, as they may be a necessary precursor to doing anything with her, as surmised from Surgeon's notes, but may also put us at great risk.
I realize that a significant amount of what I've said is largely conjecture at the moment—but I cannot say that any option currently available to us is at all free from significant risk and uncertainty. I'd like to hear what everyone else has to speak to this.