While the statement quoted in Valorum's answer certainly serves as a justification, it sounds like a quite idealized line of reasoning. In particular, the quoted text appears to have originally been published in that article in 20171, literally decades after TNG had been produced, and therefore may well be a retroactive explanation.
Instead, I'd like to suggest an additional justification:
Star Trek has an ongoing motif of the Mirror Universe:
This was very much not true during most of the time back when TNG was produced.
At that point, the only canon installment ever to touch upon the mirror universe was the TOS episode "Mirror, Mirror"2. At that time, it was a singular one-off occurrence.
Therefore, while there may have been thoughts about revisiting that universe, given that the TOS episode was fairly well-received, it's not particularly surprising this episode didn't end up with a direct sequel, like so many other TOS episodes.
As an additional reason, I'd like to point out that the mirror universe, popular as the TOS episode may or may not have been, is not an inherently viable concept when it comes to storytelling. In my opinion, virtually all sequels in DS9, ENT, and DIS are proof of that:
- First, in general, the mirror universe episodes thrive on showing the faces of our beloved characters in a very different setting. Once that surprise is gone, there isn't much left to build upon: Virtually everyone just follows the same clichés of acting as a ruthless opportunist who will betray and kill as they see fit. Nothing anything does is relevant, anyway, anyone can be killed off at any time without any emotional impact (they're all merciless villains, anyway ...) and will be replaced with the same kind of cookie-cutter villainous character by the next occasion.
- DS9's first foray into the mirror universe was interesting in that it showed a new situation compared to what TOS had presented. The DS9 sequels, on the other hand, were increasingly insignificant to what would happen to the real characters, and increasingly silly, with overblown (scaled-up) capital ships and designed just in some way to throw all the known characters (or rather, their actors) together.
- ENT's sequel didn't have any relation at all to the rest of the series, and thus, again, was just a meaningless playground.
- For DIS, with its generally darker tone, it was apparently realized that the playfulness of previous mirror universe episodes might come across as too silly. Instead, the mirror universe morphed into some overly brutal nightmare that was, IMHO, downright unbecoming of Star Trek as a whole. Ultimately, the trend that during DIS season 2, Emperor Georgiou's background was apparently more or less "forgotten" about confirms to me that the writers have no idea what to do with the purely "evil" mirror universe characters.
And on top of all that, the mirror universe doesn't make for an interesting scientific concept, either, because the idea that, in a vastly different universe, the very same people (in terms of faces and names) would be together in strangely corresponding positions (across a timespan of two centuries) seems simply too far-fetched.
Therefore, I repeat my above conclusion: While it would have been an option, there is nothing particularly surprising in the fact that TNG didn't happen to show the mirror universe.
1: Please correct me if I'm in the wrong there. Memory Alpha just links to that 2017 article for said statement, as well.
2: You mention two additional TOS episodes related to the mirror universe. However, while "The Alternative Factor" dealt with the concept of parallel (and possibly contrasting) realities, there is no reason to assume it was in any way related to the mirror universe shown on other occasions (albeit I admit, given the mess that the episode's plot is for various reasons, it is hard to make any definitive statements on what is or is not supposed to be happening throughout the episode).
The other episode, "The Tholian Web", was not related to the mirror universe at all. The episode left an open question of what became of the U.S.S. Defiant that vanished to an unknown place, but it would be a stretch to assume it was already planned back at that time that the ship had ended up in the mirror universe (and a century earlier no less), as was ultimately retconned in ENT: "In a Mirror, Darkly".
