It helps there was this sense of mystery over the Institute back in F3 as we had no idea who they were and what the Commonwealth even looked like.
Im not gonna lie, it was exciting to speculate back then. Then like most mysteries, when peeked behind the curtains, we saw the answer wasnt as exciting as the mystery itself.
The early years of F3 modding scene, before Fallout New Vegas came out, were magical. There were usually two kinds of modders, hardcore Fallout fans who desperately wanted to re-create the aesthetic that was lost in the transition between 2D and 3D(or rather, between Black Isle and Bethesda) and those newcomers who had no clue what Fallout was, but still wanted to create something interesting in it's own right. Granted, a lot of it was low quality garbage, but that's par for the course for the creation engine, point is that even within the universe of this one game, people still made some really interesting mods and stories/characters. Lore friendly? Absolutely not, but at the time, the fans didn't even know if we should consider Fallout 3 canon at all so it didn't matter. That debate got a bit louder when New Vegas came around and all of a sudden, we had to take Fallout 3 into more serious consideration since a few bits from that game were mentioned in NV. That's also when I think that charm of creative mods from new players ended, since the game was solid enough on it's own most mods looked worse than they actually were since they were contrasted with the base game. The highs were better, but the lows were lower, see the current NV modder base and slop like The Frontier. At that point, as the years went on, it also became clear that the Fallout IP wasn't getting any better and the once cute and naive newcomers became obnoxious, clueless tourists who despite having easy access to the original titles and NV chose to ignore them and only focus on Bethesda's lore, ie Fallout 3 and later Fallout 4. Then 76 and the TV show came out, I reckon you know how bad the fanbase got by that point. Divide got bigger between the two groups, optimism about the IP and it's future faded, both sides are stuck with endlessly modding their one game or grinding 76 with nothing new on the horizon except another season of an awful Amazon show. Say what you want about Fallout 3, but back then, future of the franchise at least raised optimism about where it could go now that it had proper funding and a studio that can manage the IP, people were more carefree with what they put out as far as modding goes and tribalism between the fanbases wasn't nearly as bad. I don't think we can ever go back to those times anymore than we can go back to the 90s and make sure the IP is safely hidden from the mainstream tourists due to it's obscurity.
Funny that you mention Institute in Fallout 3, I believe there was a mod that actually added the MIT(not CIT) and the Institute into Fallout 3, but then it became 100% fanfiction when Fallout 4 came out and the official take on the faction was nothing like the modders imagined.
At least the Big MT's dumb ass experiments were excused by the fact the ones behind them were mentats addicted brains in jars with all the in the world and no moral responsibility to back it up.
I think the biggest complaint of Institute is that, in execution, it is indeed just a poor man's Big MT. Institute as an idea is fantastic, but as usual with Bethesda, execution falls flat on it's ass. Fallout 4 deserved a better hook than muh son and muh robot rights.
Biggest issue with Fallout 4's factions is that there's no truly evil faction. At worst they're misguided.
I understand they were trying for a New Vegas style grey morality but they lacked the talent to pull it off and no matter what type of character you're playing as it feels unsatisfying.
If you're an evil sole survivor it feels unsatisfying became none of the factions are truly evil so you can't actually be a bad guy or make evil decisions.
If you're playing a good guy it feels unsatisfying because since none of the factions are truly evil you didn't triumph over evil or accomplish anything for the forces of good.
Base game factions don't really let you do anything evil, but there is ways around it. Nuka World adds the raiders as a possible faction, and sure they're more of a guild than a proper faction but they at least let you do some proper evil roleplaying(there is a reason they're not big enough to tackle Brotherhood/Institute on their own and need help from other factions, but the reason for siding with them is less black and white when you're running your own gang and have to consider how geopolitics effect your takeover of the region). I will tell you, raiding the Commonwealth is infinitely more satisfying then clearing out random packs of raiders or ghouls for some ungrateful dirt scratchers who can't even follow basic orders when asked to fight(or follow a chain of command, for that matter. Your title of a "General" for the Minutemen might as well have been pulled out of a cereal box for how much it matters).
Then there is the fantastic America Rising 2 mod that adds Enclave as a full fleshed out evil faction, with it's own nuances and choices, and with them you can properly side with the faction for the entire game with it's own main questline.
I already linked it, but the Valkyrie mod adds some permutations for the vanilla main quest, letting you experiment with morality a bit more freely like you could with the older games instead of being railroaded into stupid decisions that make no sense.
https://www.nexusmods.com/fallout4/mods/28085
Your only option for an evil playthrough (Nuka-World) is just reskinned Minutemen busywork in the end, and you can't even finish the game with them.
I disagree, Nuka World has it's own proper main quest(ie the raider faction main quest) and the busy work with settlements is only there at the late stages of it. Not only are the rewards better, actually giving you a reason to set up raider camps, but you also get the opportunity to finally put the useless niggercattle farmers you would normally be doing bitch work for under your boot and heel. I modded the game so that every single settlement can be raided, that includes The Castle, and I took over the entire world map. This includes dozens of modded in settlements all over the game world, it was so satisfying to have every inch of the game map under my strict control. If you want to go further, there is a mod that lets you blow up all major faction HQs(that includes destroying Diamond City for a complete anarchistic playthru), it plays really well with a raider playthru.