In S01E10 of Star Trek: Discovery Burnham notes that the USS Defiant is believed to be the first ship from the prime universe to arrive in the mirror universe. However, the Defiant comes from Discovery's future, specifically the TOS episode "The Tholian Web" which occurs around a decade later.
So when the Discovery crew returned to the prime universe, why didn't they warn Starfleet about the Defiant and prevent the events that lead to its loss and the death of her crew?
The conclusion of the 2nd Season of Discovery shows that all reference to the USS Discovery, its missions, personnel and technology are expunged from the record of the Federation.
In Universe this extends to the very existence of the crew as historical fact. Spock appears not to have a step-sister, rather than having one that died or disappears in some other incident.
The record of what happened to the Defiant would be removed in the same purge.
Regulation 157, Section Three, requires Starfleet officers to abstain from participating in historical events.
Any residual trace or knowledge of Discovery's data, or the time suit, offers a foothold for those who might not see how critical, how deeply critical, that directive is.
Therefore, to insure the Federation never finds itself facing the same danger, all officers remaining with knowledge of these events must be ordered never to speak of Discovery, its spore drive, or her crew again. Under penalty of treason.
Additionally, the journey of the Defiant to the Mirror Universe, and back in time, represents a stable time-loop featuring the Discovery crew. Without the Defiant reaching the past of the Mirror Universe, the course of history there would be significantly changed and given the cross-over back to the main Universe of Gabriel Lorca and Philippa Georgiou, the history of this side would be affected as well.
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. The arrival of Defiant in the Mirror Universe was key to the Terran Empire's victory over rebels in 2155 ("In a Mirror, Darkly, Part I"; ENT 4x18) and the Empire's subsequent development. Therefore, the Federation will always need for the Defiant to travel to the Mirror Universe exactly as it happened.
