Speaking of intellectual dishonesty you're going to need your dancing shoes on for this one. I figure Discovery will go to the mirror universe with their spore drive if they are not there already. Looking at these dialogues from DS9 "Crossover":
INTENDANT: After the first crossover, we were afraid that others might come to interfere in our affairs. It was decided then that if it ever happened again, we would promptly dispose of anyone who appeared from your side.
QUARK: Didn't I hear somewhere that a transporter was involved in the first crossover?
KIRA: I did ask him about a transporter, that's true.
INTENDANT: But why?
KIRA: You know I'm looking for a way back. A transporter was responsible for the first crossover.
You're assuming that DSC's trip to the mirror universe will become public knowledge. Seems a bit hasty. I mean, you don't seriously think Lorca's going to put this in his official report to Starfleet, do ya?