The Federation depends on the Terran Empire

In "The War Without, The War Within" (DIS 1x14), deposed Emperor Philippa Georgiou gave Starfleet advice on how to win the war against the Klingons, based on the Terran Empire's successful conquest of Qo'noS in the Mirror Universe. Using this advice, Starfleet brought the war to a swift end on good terms for the Federation.

The Federation continued to benefit in "Such Sweet Sorrow, Part 2" (DIS 2x14), when warships of the recently-stabilized Klingon Empire led by Chancellor L'Rell fought against Control's Section 31 fleet.

Former Emperor Georgiou will be the lead character in the upcoming (as of summer 2019) Section 31 series. As part of Section 31's restructuring in the wake of Discovery season 2, it seems that the Federation will continue to make use of Georgiou's brutally practical approach to problem-solving.

The Federation needs Georgiou, so the Federation needs the Terran Empire's history to remain intact, and Georgiou herself would certainly oppose any plans that could completely obliterate her own personal history. Therefore, the Federation will always need for the Defiant to travel to the Mirror Universe exactly as it happened.