There are good reasons you’re just ignoring them.
Okay, what are they?
Starfleet probably didn't want word getting out that they turned command of their most important asset in the war against the Klingons over to the evil twin of one of their captains, despite numerous red flags that something was wrong with him...
Yeah,
that part I can see keeping on the DL. But even so it would be simpler merely to record that Lorca was killed in the MU (or just went MIA, if they want to hedge their bets, since for all they know the original may still be alive) and just fudge the details of which Lorca they're talking about.
(And, of course, one might also think that having dodged that bullet with Lorca, they wouldn't double down and repeat the mistake
deliberately with Georgiou. But go figure...)
And honestly, in light of that, how practical is it to say the MU could be "classified" at this point, anyway? The Georgiou decision indicates that the Starfleet admiralty (at least Cornwell, and probably others above her head), the Federation Council (and that's a lot of politicians, and politicians gossip, and also look for things to investigate), and Ambassador Sarek... plus of course the entire crew of the
Discovery from Saru down to the lowliest cadet... know about the existence of the MU. No matter what label you stamp on it, that is not a good starting point from which to try to keep a secret.
Hell, where is Starfleet going to say the ship disappeared to for nine months, if they can't mention the MU? I assume investigative reporters still exist in the 23rd century...
...It actually makes one wonder why, in universe, they allowed it to be public knowledge later on...
That was kinda my point. If we actually buy the rationale offered in DSC, then it shouldn't have been public knowledge later on... but we know that it
was. Basically the writers painted themselves into an impossible corner: they had to keep it secret to be consistent with the continuity of "Mirror Mirror," but the very act of doing was inconsistent with continuity
after "Mirror Mirror."