This was silly, and begs the question of why the Mirror Universe was not classified a few years from now when Kirk and friends cross over....?
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Because that was NOT in the aftermath of a major war where the Federation had suffered "terrible losses." It was a different climate, so the Powers That Be made a different decision. A decade later, they took a different approach--which is how things work in real life. Policies and leadership change over time, particularly in response to major crises, wars, etc.
Yes, of course, it's not logical to think that the MU version of your dead daughter is the same person, but, again, human beings are not inherently rational creatures, especially where dead loved ones are involved. Just look at the huge boom in Spiritualism after the "terrible losses" of WW I.
Hell, even Sarek admitted that his logic was "uncertain" where his son was concerned. Starfleet's concerns seem plausible enough to me. One can debate them, but I can certainly believe that such arguments prevailed, at that time.
Ten years later, it was a different story . . ..,