TMP is anything but irrelevant. If anything, it contains the one event that's had more lasting impact than anything else in any Trek movie: Spock's epiphany about the value of emotion. In every Star Trek production where Nimoy's Spock has appeared from TWOK all the way through the 2009 film, he has been portrayed as a character who's at peace with himself, who's restrained in his emotional expression but not actively resisting or denying his emotions, who advises others that logic is not the end-all and be-all of wisdom and that it can be okay for a Vulcan to feel. And that comes directly from what Spock went through in TMP, completely changing him from the insecure, brooding young Spock who was constantly at war with his emotional side.
Is there anything else in any Trek film that's had such a lasting impact? Sure, Spock died in the next film, but it was reversed by the very next movie, and it essentially had no lasting consequences. The Enterprise was destroyed in the third movie, but then they got another one that looked just like it. Chekov moved to another ship, but then he came back. Sulu got another ship, but that was the last TOS movie. Kirk died, but that was after the last TOS movie, in a time when he'd already been presumed dead anyway, so it can't really be said to have that great an impact. The TNG crew lost their ship, but then they got another one. Riker and Troi got a new ship and Data died, but that was the last TNG movie. Essentially, every other major change in the Trek movies was quickly rendered irrelevant and devoid of consequences either by its reversal in a later film or by the cessation of the film series as a whole. But Spock's life-changing epiphany in TMP has affected every Spock story for the subsequent 30 years.
TMP has lasting impact in a lot of other ways, too. It was the first Trek production to include a security chief (Chekov) among the regular cast and a dedicated tactical station on the bridge, a precedent followed in every subsequent series. Its characters of Decker and Ilia were revamped into TNG's Riker and Troi. It established San Francisco (and specifically the Presidio) as the home of Starfleet Command for the first time. More fundamentally, it was our first glimpse of Earth in the Federation era, setting a precedent for Earth-based stories which was followed by multiple subsequent films and episodes. It thoroughly reinvented ST production design and technology design in ways that have influenced all subsequent productions. It brought Jerry Goldsmith into Trek for the first of many times and introduced his main title theme, which is almost as closely associated with ST as the Alexander Courage theme.
So if anything, I'd say that TMP is still the most important and influential Star Trek film to this day. Only TWOK and ST 2009 come close to the same level of impact. Their impact may be more obvious than TMP's, but not quite as pervasive.