Tough one to answer. I can tell you that right from the jump I thought the main storyline wasn't gonna be great. So much I could get into there. The whole thing is basically a whole meme from start to finish. It's the most ridiculous, ineffectual, and campy thing I've encountered in a good while. Just really weak, all around. That was supposed to be the most serious side of things, showing how harsh the world really is and laying down the core themes... but being as weak as it was, it left only all of the goofy shit to prop things up, which made the whole game feel like one big joke. Fallout has always had quirky humor, but if that's all it ever had going for it, it would never have gotten the following it did to begin with.
The briefest way to describe it is as a collection of great ideas missed out on. Between all of the potentially interesting characters and potentially interesting factions, and the dearth of preexisting lore already available for all of this stuff, a lot of cool things could have been worked in. But it was almost more written to make you feel like things were always happening, without much of anything actually happening. There is constant motion with all of these different plot points and one-note factions (that's a big issue for me, too,) and yet, I have a hard time caring.
Seems like they've always struggled with that... since Skyrim at least, and Oblivion to a lesser extent. I think FO4 was where they really started watering down the themes of the franchise. The little stories you can discover, that are never directly told, are much more interesting... if not for that nagging irk of reading implausible terminal entries. Sometimes all I could think was "If this was true, why would anyone write about it in a terminal?" They got lazy with that, IMO. Hard to imagine that people were such serious historical documentarians, constantly putting minutia onto holotapes for nobody. What happened to "Show, don't tell" anyway? Even in Skyrim, I remember reading books and notes for those little mystery-style scenes and still not fully getting it until I explored it another time... because the whole story wasn't spelled out right there. It was more important to explore and contemplate the world... often you needed that context to decipher the possibilities for what may have happened. You often had to bring in things from elsewhere.
There was an actual give and take, you know? In FO4, you just run the holotape and that's pretty much it.
Still, that stuff added much more depth to the FO4 world than any of the main stories or characters did, for me, even only being relegated to self-insulating little tidbits. Far Harbor was a welcome departure, with a much better fleshed-out world revealed directly through the stories and characters. I enjoyed that. If the whole game was on that level of writing, I would take it more seriously.
Otherwise, I don't think it was particularly egregious like many others do... just very, very uninteresting. It shouldn't be that way with Fallout! Fallout worlds, while bleak and dark as hell, were very 'colorful' lived-in places. I didn't get that from FO4. Every group is like a hivemind collective, with one or two defining attributes that are never deviated from among its entire composition. That defining, micro-level conflict just isn't there... the stuff that makes you contemplate why certain things are... or reflect on things you didn't consider.
Take Strong, the helpful super-mutant. He's there to show you that not all super-mutants are the same. But strong is not different from the others... he's so dumb he thinks the milk of human kindness is a real thing. So he sides with humans... in pursuit of that same childish notion of strength and dominion. All of them are exactly the same, which is not how super mutants are by definition. Some are basically just big, dumb, hulk-ass mutants, but some were more intelligent than humans and even beyond intelligence they were complex beings with all sorts of history and a gamut of unique qualities... this stuff is there to work with already! But instead they disregard it to make them all dumb rocket-fodder. They're barely alive at all. What, am I supposed to believe they just hang out in ruins all day and wait for humans to shoot? Because that's all I ever see of them. If we're talking about building this big, lived-in, post-apocalyptic world, that's not very compelling or convincing.
This is just one example. Everything is kinda like that. All of the factions and towns are like that, too. Every person is singular in purpose and never is any real nuance built up through them. You learn a little more about them, annnnd.... none of it means anything. In the older games, you learned a ton about the world itself through the characters and the groups. And the experience was seamless.... you didn't consciously notice how it was inserting the world into your head - it wasn't earmarked or beat over your head. In FO4, they were all just sort of there to move you through the game. Just drilling the same basic things into you over and over again. It's all just used to direct you to places and mechanics. There's a certain way they want you to play their open-world game, and the writing serves only that.
Bizarre when you have so much interaction in a game and it still feels implacably empty. I still enjoy a lot of the lore, but on the whole I don't particularly care for the writing at all. I hate using terms like this because of how non-descriptive they are, but all I can think to say is that it feels insincere. Too many ideas fail to justify or substantiate their existence at all. There is very little I toss-out in ES... but I find myself dismissing a lot of things in FO4, just because they are useless. Everything is just kind of there and it's like "Welp, there it is! Yep, that's wanna them Fallouts, for sure."
I think the big problem has to do with Bethesda's general writing approach. It works for some things... they basically come up with a lot of elements that are sort of a mix-n-match affair. It can work as a strength... all of the mystery and unreliable narration can pull you in and get you using your imagination. But it's no good for cohesive worlds/storylines. With FO4 they tried to create a more definitive pipeline with a pretty set timeline full of concrete/definitive stuff. And while being only mediocre at that, it also sucked a lot of the fun out of exploring and experiencing that mishmash, emergent side of the world. It feels awkward, the way it always tries to tether you. I think they tried to play it safe with the level of direction and just screwed it all up. ES games work as grab bags, because that's kind how they've always been structured, and it's a BIG bag with a lot of stuff in it. Fallout wasn't originally that way and I think trying to start from that and do more of their own thing with it just holds the whole thing back.
I honestly don't think they have the chops to write a good Fallout game... not even for their most successful gameplay models. Not geared for it at all. Definitive exposition WITH choice-driven gameplay and worldbuilding just isn't their strength. Never really has been, but it wasn't as much of an issue, as it was so little of the focus that you still had a full game if you ignored most of it. They could get away with shallow writing for the hashed-out stuff because that's not what anybody plays their games for - it was just a basic skeleton - a couple of paths you could take to get to the real attractions in the game. That's probably why people play it over and over again... past a certain point they don't care about the story anymore. The writing did not exist simply to tell that story and if anything the story was a small part of the writing. People enjoy the world and lore gotten elsewhere. But it's like in Fallout, they abandon that side of the writing to try to show you something specific, which it just so turns out they aren't great at. Not surprising... nor necessarily pessimistic... just saying they bet on the wrong things to make the writing fully work for those games. They wrote the wrong stories for FO4.
It's cliche to say, but Obsidian had a better grasp of storytelling by miles. That felt like a Fallout game with Bethesda gameplay. It was great for Fallout and Bethesda fans alike and made for one hell of a proof of concept for a good, open-ended 3D Fallout. FO4 feels like an ES title with all of the soul sucked-out, and Fallout stickers slapped-on. "Elder Scrolls with guns." Only this time they tried to make the core story the whole focus, forgetting that they didn't know how to write one and also retain the strengths of past writing from their beloved ES series. They took the worst from both when they tried to do that.
I think in a non-Fallout game, a lot of the things they tried with FO4's writing could have worked... but what they wanted to write was both holding back and being held back by Fallout itself. It just made no sense to me, why they would choose a Fallout game to try the things they did with the writing.
As time goes by, it's becoming more obvious to me that nobody writing for their Fallout games has any connection to the source. The way everything is written, it's like they do understand what Fallout is on superficial level, but really ONLY on that level... and they just pumped FO4 full of that, ad nauseum. Always telling you it's a Fallout game... never giving you a chance to dive in and experience it as one.
ES has had it's saving grace in the fact that Michael Kirkbride still contributes to the lore pool pretty heavily, in spite of not officially working for them. He loves that shit and has written some of the most brilliant lore the series has had to offer. Fallout doesn't have its own Michael Kirkbride...
It's like how in the fantasy genres there's this deeply embedded practice of taking Tolkien's tropes/archetypes and building something completely out of those things, without using them to thier full potential or inserting enough interesting new ideas to give the work a reason for being, let alone standing anywhere near Tolkien's own works. But if you do that, people will, at a minimum, call you a fantasy writer. The older Fallouts are Tolkien's writing. The newer Fallouts are to that what "generic Tolkien loveletter #1036938." is to Tolkien himself. And people do call it a Fallout game. Fallout 4 is a loveletter to a body of fiction that already changed its phone number.