By the way, I never complimented the video in the OP. I considered doing something similar myself, but quickly abandoned it as far too much work!
Back on-topic... ...Would we really care all that much over the torpedoes and stuff if they hadn't said that they had a limited number of them? Would we be complaining if they found some alien repair tech that could easily regenerate hull damage? Would we be complaining if Voyager had been some huge alien starship and they never explaining just what the ship could do?
No, no, and depends. If it's worth spending time telling us that they can't do something, then it's worth spending time telling us that that's no longer the case, especially when only a single line would have been enough. Otherwise, it comes off as a spontaneous retcon, not completely unlike Chuck Cunningham Syndrome.
But that would mean using the C word, continuity. But I agree with you, all it would have taken is a few lines not much to ask was it?
Basically, it comes down to TOS, TNG and DS9 getting away with the same stuff because they never bothered saying anything that could limit themselves. VOY get critiqued because they mentioned or or two lines limiting themselves (even if those lines made no sense). I mean really, even if they had mentioned "Yeah, we found a way to trade for more weapons." then the most likely response would be that they didn't make a 10 episode arc out of how to make new torpedoes.
And the fact that TOS, TNG, DSN took place in or near UFP space. So it's easier to rationalise that they visited a starbase or another ship came to them with new supplies. But it is not the audiance's fault (or part of it) for holding them the procducers to they limits they themselves put in. It's quite simple if you aren't going to keep to your own limits, don't put them in to begin with. It's sloppy storytelling to simply ignore them because they are inconveniant. Sometimes having limits can make for more interesting storytelling.
Sure, if the limits actually made sense. The problem was, the limits they put on VOY didn't make sense to begin with. I fthey said that the Warp Drive was damage and they couldn't go very fast, then that would've been a limit that made sense and it would justify them sticking around so to flesh out the area. But stuff like not being able to make new shuttles or torpedoes? That stuff didn't make a whole lot of sense.
But it doesn't matter if the limit makes sense or not. From a storytelling point of view don't place a limitation if you intend to ignore it. Sure you can overcome a limitation but it does a disservice to your audiance/reader not to explain why the limitation no longer applies. Technology has it's limits, after all you could say why not just build a massive replicator and replicate entire ships rather than construct them from scracth. So TNG and DSN went through numerous shuttles, well given the size difference between the Galaxy and Intrepid Class we would expect the Galaxy Class to carry more aixillary craft. In the very first episode of DSN, DSN recieves is three Runabouts from the Ent-D, so we can logically say that replacements arrived the same way. A loss of shuttlecraft/crew member etc.. should have had an impact of some sort, but none of that was evident. They were missed storytelling opportunites.
I think the limits made enough sense. I already discussed why upthread. Perhaps there are certain critical materials that they were absolutely not initially equipped to replace on their own, under any circumstances, until they could create their own industry, including industrial-strength replicators, refining processes, etc. We don't really know, because they never said, but I don't consider the idea to be implausible at all. Here's some examples from Forbidden Planet. In order to communicate with Earth, the C57-D had to be partially disassembled, in order to make the powerful transmitter required, which wasn't standard equipment. There was also a "Klystron frequency modulator," that their technical manual said couldn't be replaced and that, once sabotaged, they set out to try to rebuild.
Yes, it was a plot device, because it kept the ship planet-side and rendered them vulnerable to attack by the id monster. That aside, my point was that the limitation came across as completely plausible in-universe, because their FTL was a pretty big deal. Their main drive had to be taken out of the ship just to power the transmitter. In the case of Star Trek, the limitation could be anywhere from raw power requirements to rare but critical materials that can't be replicated with the equipment that they shipped out with. On Voyager, one could imagine that certain interior sections of the starship near engineering had to be repurposed with equipment that they cobbled together either from spare parts, cannibalized equipment, or parts that they acquired by trade. The ship wasn't originally designed for a mission with a duration of 70 years. On Gilligan's Island, they built a lot of things out of bamboo and coconuts that weren't initially on the Minnow.
And yet somehow they were able to rebuild it despite being on some abandoned world without any external aid. Try that with Voyager, and the only response will be that whatever it was they were trying to replace, they shouldn't have been able to replace it at all and have to go the entire remainder of the series without. The show would've been better off if they'd been on some massive alien starship they got from the Caretaker's Array, maybe an automated ship that didn't need a crew, and they never actually specified just what the ship could do in the first place so there'd be no limits.