Would Lt. Nog have a secret note for superior officers reviewing him that says, "Promote promptly. Known to be a successful Federation starship captain in an alternate future"? Would James Kirk (Prime AND Kelvin) have a note that says, "TOP PRIORITY: Due to classified knowledge obtained during various temporal incursions in Earth history, promote to captaincy as soon as feasible"? Would Ensign Kim have one that says, "Watch carefully, and put through psych eval for every advancement in rank. Known to be a Federation starship captain in another timeline, but in that timeline was complicit with treason committed by that timeline's Admiral Janeway." And for that matter, just how in the world did Starfleet decide to still decide it was a good idea to promote Janeway to Admiral, when they had to know what she did in that alternate future? I sometimes wonder how much future knowledge Starfleet is working with, behind the scenes. Perhaps we've had that question about where the Enterprise-A came from wrong the whole time: maybe she wasn't the Yorktown or the Ti-Ho or some other ship with a paint job to change the name. Maybe Starfleet knew to start building a new Enterprise in time to be ready for that point in time, and she really was a whole new construction...
True... but even DTI would presumably be telling them that some of this is Predestination Paradox. In which case, they'd still need to act on it. Maybe?