The reason the USS Enterprise missed Star Trek: Deep Space Nine's Dominion War. The main conflict of the Dominion War coincided with the time frame of Star Trek Insurrection, when Picard and his crew protected the Ba'ku and the Briar Patch from being exploited by Starfleet iral Dougherty (Anthony Zerbe) and the Son'a. The war was ultimately won by the coalition of Romulans, Klingons, and the United Federation of Planets led by Captain Benjamin Sisko (Avery Brooks).
Of course, the real-world reason why Picard and the Enterprise - the Federation flagship - didn't take the lead in the Dominion War is because the Dominion War took place entirely on DS9, and it was a storyline executive producer Rick Berman wasn't fond of. Except for Worf (Michael Dorn), who was part of DS9's cast, TNG's actors were not asked to appear in the TV series. Despite the lip service paid to the Dominion War in Star Trek Insurrection, the lasting impression is that the Enterprise-E sat out the pivotal conflict that decided the fate of the Alpha Quadrant, and there was no in-universe reason given as to why except for non-canonical Star Trek novels.
Discovery Set The Precedent For The Enterprise-E Missing The Dominion War
However, the 23rd century USS Enterprise commanded by Captain Christopher Pike (Anson Mount) missed Pike's Enterprise back to fight the Klingons. Her rationale was she feared the Federation would lose to the Klingons, and she wanted the Enterprise to survive and represent the best of humanity in the worst-case scenario. John Jackson Miller's novel The Enterprise War, which may be canonical, fills in the details of where Pike was during the Klingon War.
The logic of why Pike's Enterprise was withheld from the Klingon War is a precedent that could explain why Picard's Enterprise-E wasn't in the thick of the Dominion War's fighting. Star Trek Insurrection saw the Enterprise-E still performing diplomatic missions during the war, and perhaps the decision was made to keep the Enterprise out of the Dominion War for the same reason as Pike's Enterprise. The Federation was in grave danger of losing the war, and it makes sense that the flagship was too valuable and important to risk on the front lines against the Jem'Hadar. Even if Picard's Enterprise did its share of the fighting, it still wasn't in the major battles fought by Captain Sisko and the USS Defiant.
Is The Enterprise Still The Flagship In Discovery's 32nd Century?
The Enterprise has been mentioned but not yet seen in Star Trek: Discovery's 32nd century, and it begs the question: is the Enterprise still the flagship of the Federation? After all, the USS Discovery has emerged as the most important Starfleet ship of the 32nd century, and Captain Michael Burnham (Sonequa Martin-Green) is called upon to deal with the most pressing galactic crises. Of course, this is because Star Trek: Discovery is about the eponymous starship, but the status of the Star Trek: Strange New Worlds' retcon means the Enterprise has an unbroken legacy as the Federation flagship. It would be a shame if the USS Discovery or another starship supplanted the Enterprise's status.
Star Trek: Discovery Season 5 is expected to premiere in 2023 on Paramount+.