At one point, Quark (Armin Shimerman) from Star Trek: The Next Generation movie didn't involve Captain Jean-Luc Picard (Patrick Stewart) and its crew confronting the Dominion in any way; instead, the film told a lighthearted, standalone tale that was jarringly out of place while the rest of the United Federation of Planets was in the midst of a devastating war where millions died.
In Star Trek: Insurrection, Captain Picard went against the orders of Starfleet iral Dougherty (Anthony Zerbe) when he sided with the Ba'ku, a race of 600 people living on a planet in the Briar Patch. This region of space had regenerative properties that kept the Ba'ku from aging — essentially, it was a "Fountain of Youth" that the Federation sought to harvest with the help of the Son'a. Meanwhile, the Nog (Aron Eisenberg), lost his leg at the Siege of AR-588 but he heroically battled back from his injury and despair.
Granted, the Picard fought the Borg in Star Trek: First . But a front-and-center appearance by a major DS9 character like Quark would have been a nice visual reminder that the Dominion War was still going on, even if Quark was humorously trying to find new avenues of profit far from his bar on Deep Space Nine.
After all, if a fan only watched the Jadzia Dax (Terry Farrell) wasn't happening.
Watching Star Trek: Insurrection, it seemed as if Picard and his ship didn't fight in the war at all since the crew and the starship were immaculate. While there have been Star Trek novels detailing the Enterprise-E's activities during the Dominion War, those are apocryphal. In of canon, Picard and the Enterprise-E's lone appearance during the Dominion War had them chasing the Fountain of Youth as the rest of the galaxy was suffering.
The Quark scene deleted from Star Trek: Insurrection would have also set up U.S.S. Defiant nearly being destroyed in that movie), and it would have also forged a stronger link between Captain Picard's latest mission and the Dominion War that engulfed the rest of the galaxy.