Anyone who says FO4's story is intolerably bad is either new to video games or is flat out lying to themselves about the quality of storytelling in the medium. I realize this is a supremely controversial opinion that's bound to receive many colorful reacts, but I've stood by this belief ever since the game's release. Yes, I hate the forced backstory, voiced protagonist, and dialogue limitations but that's not unique to RPGs nor even a dealbreaker for Codex judging by many of the favorites around here. But a lifetime of playing games has trained me to slog through cliched, cringe-worthy writing. Most game stories simply aren't that good. When I've revisited some childhood favorites, the narrative is rarely what holds up best. In fact often the greatest strength of narratives in older games is how little they lean on it throughout the playthrough. Even Fallout 1 and especially 2 can feel like an R-rated Teenage Mutant Ninja Turtles sometimes.
Fo4's story is intolerably bad. The fact that videogames in general are bad doesn't alleviate the direness of Fo4. But more to the point, I think you're doing two things here - firstly conflating "story" and "setting", and secondly underestimating how important these two concepts are for the success of a Bethesda-style game.
The game has a serious issue at its core - the vast bulk of the gameplay is intended to be self-directed exploration, where the player seeks out dungeons of his or her own accord and delves inside. The earlier Fallout games obviously didn't have to grapple with this, because they didn't have a similar gameplay model - players spent most of their time in dialogue or exploring non-combat zones such as towns, and doing quests. New Vegas recaptures some of this by treating the overworld as basically an afterthought, and sets up the game so that the player is directed from quest to quest, with self-directed exploration being largely optional and a way to voluntarily shake up the gameplay between story-based content.
Fallout 4 rejects the need for a coherent setting or interesting quests or anything else of the sort, because they decided to make an open world combat game, not a game in the vein of the original Fallout games. Alright, that's fine - let's take a look at Fallout 3, which largely did the same thing.
For its myriad problems, Fallout 3 achieved acclaim in the mainstream, if not on the Codex or NMA. For many, it was their first foray into Fallout, and while we can sit here for hours and rightly rip apart Bethesda's impression of the Fallout world, Fo3 still paints a visually and thematically exciting world full of strange characters to meet and peculiar situations to encounter. To pick an illustrative example: the subway vampires. To a fan of the previous Fallout games, they're cringeworthy and tonally jarring, but to a newcomer, they're another fascinating addition to the game's vaguely surreal, almost psychedelic world. It's something memorable and unique, and it encourages the player to press on with the dungeon crawling that forms the bulk of the gameplay - if this subway has vampire cannibals, what might the next dungeon hold? (The answer is "nothing" but you don't realise that during your first playthrough)
Fallout 4 is so grim and boring that it fails to recapture
anything that worked in the previous Fallout games, not even achieving Fo3's veneer. The world is samey and dull, the factions are not only badly written but also boring even at the conceptual level, and everyone you meet in those factions is a total void who might as well be replaced by a cardboard cutout with "TWAT" written on it. The only characters I even remember are Piper (boring twat), Danse (boring twat), Preston Garvey (Satan) and Kellogg (inexplicable twat). The synth plot is dull enough to induce comas, the Minutemen are a fucking irritant, and the game only has one actual town - and the less said about it, the better. Even the world design itself is a drag with scarcely any memorable locations. Fallout 3 and Skyrim, for their many faults, had striking and unique dungeons at times (that one where you fall through the floor in Skyrim, the street laced with mines in Fo3, etc). Fo4 feels like it was made by procedural generation or something, it's just a few rooms recycled over and over with fuck-all inside.
Few people are going to want to explore a world so empty and a setting so lifeless. Why go delving into another boring-ass subway if the game isn't even bothering to sell you the lie that you might find something of interest in there? You can actually feel the boredom and lack of passion of the overworked, miserable designers seeping through into the game. It's not just that the story and setting are bad (though they are), it's something much worse - they're dull. Fallout 3 was retarded but enjoyed widespread acclaim because, whatever you might say about the nonsensical story and world, it definitely wasn't boring. People were excited to see what lay around the next corner, to discover strange landmarks like the town with the minefield, to find Dogmeat in the scrapyard, to stumble into the village with that weirdo who likes Nuka Cola. Fallout 4 can't incite the same response in the player, and doesn't try. This is the reason, I think, that even mainstream gamers - the same people who very much enjoyed Bethesda's previous offerings - were lukewarm at best and hostile at worst towards Fo4.
To this day I don't know what they were thinking. "Open world shooting game with crafting and perks" was already done by the Far Cry series, which cornered the market and is leagues ahead of Fallout 4. They made a really shit, clunky version of Far Cry with far worse shooting and "Legendary" monsters who slow the gameplay to a hideous crawl whenever they pop up. Absolutely pointless project, waste of time, money and effort. All they had to do was make Skyrim with guns, or another Fallout 3, and they somehow dropped the ball so spectacularly that they more or less killed the franchise for (what's shaping up to be) at least a decade.