It's a highly logical determination that would likely save a lot of hardship, to say nothing of franchise continuity. That is, if not for the existence of Emperor Georgiou in the Prime Universe, and the capture by Klingons of Starbase 1 -- "our only remaining sanctuary" -- which presumably is where Discovery's files were to be locked down and destroyed.
Although the emperor wishes nothing more than to be returned to the Mirror Universe, the fall of Starbase 1 forces Burnham, and Cornwell, to resort to more extreme tactics, to match those employed by the Klingons. Georgiou, who defeated the Klingons in her own reality, offers a possible way to end the war: by launching an elaborate large-scale attack on their home world, Qo'noS, which involves Discovery jumping to within a global cave system in order to map the planet's surface.
But with the very existence of the Federation at stake, Starfleet must take another enormous risk, in entrusting the Terran emperor to execute her own plan -- only as Captain Georgiou, whom Discovery's crew is informed was merely presumed dead. In Starfleet's new fiction, she had instead been taken captive, and was only recently freed from a Klingon prison vessel in a daring raid. Of course, we need only look to Ash Tyler/Voq to see how the last "POW" worked out for Discovery.
Or, y'know, Lorca's longer-term charade. But, desperate times and all of that.
In the end, it's likely Georgiou's role in the defeat of the Klingons (the Prime Universe version, that is) will be relegated to the ash bin of Starfleet history, alongside Discovery's spore drive, the true identity of Gabriel Lorca, and Ash Tyler's time as an enemy sleeper agent. However, considering the number of people aware of part, or all, of that ever-growing conspiracy (including the random transporter operator who beamed aboard Emperor Georgiou), there would appear to be few guarantees that those details remain secret. Unless, of course, Discovery and her crew were to ultimately perish in the defense of the Federation ... and for the sake of franchise continuity.
Airing Sundays at 8:30 p.m. ET on CBS All Access, Star Trek: Discovery stars Sonequa Martin-Green, Doug Jones, Anthony Rapp, Shazad Latif, Mary Wiseman, Wilson Cruz and Mary Chieffo.