I find the hand-waving dismissal and justification here kind of ridiculous, really. As
@Captain of the USS Averof pointed out, this is the most powerful device we've seen any single human posses on Star Trek.
EVER.
This isn't normal time travel or transwarp beaming or whatever other nugget of lesser value someone throws out.
This is a whole new level. The fact that it was localized or only lasted for a half-hour minutes doesn't change the fact that it's still allows a person to posses power the likes of which the franchise had only ever given to a quirky mischief maker who's now partying with ponies.
And as for the limitations, all we know is that the crystal Mudd had worked that way. For all anyone knows, the technology could be capable of chagrining much longer periods of time at much greater distances. And that's kind of the problem. The writers did such a poor job of framing it - which is dismissing it as just another "plot device" is really reductive and excuses poor writing.
Because when you talk about the really great uses of such powers in all of science fiction, there are always rules and consequences to breaking them. Warp drive has rules. Transporters have rules. And yes time travel has rules and Star Trek has always presented consequences whenever someone goes and fucks with them, even when "time travel" is just the plot device.
Heck, take something like "Assignment Earth"; The time travel used in that episode was about as "plot-devicey" as it gets. The whole point was to put the Enterprise crew in a soft pilot for a different show. But then the episode became about how Kirk and Spock got in the way and mucked things up, and there were had consequences, so the new guy had to fix it all.
But let's just take time-loop episodes. I've already shoe-horned "Window of Opportunity" into this thread, so let's start there. It's been a while since I last saw it, but I do remember Samiel making a point at how they essentially altered a good chunk of the galaxy and alluded to the dangers of such a super powerful device built by God-like aliens. (Who, for-example, had their own after-life.)
Closer to home, "Cause and Effect" ended with the image of Captain Frasier, Grammer K. dressed in attire and flying a ship from the Original Series films. It was an image that so simply carried the weight and magnitude of what had happened that even a casual fan could pick up on it. So this only goes to show that, if done well, you don't need a lengthy expo scene to lay down the ground rules and consequences for breaking them.
But they gotta be there.
And no, this isn't about canon or any bullshit like that. This is about building a foundation for credible story telling