Sure, almost anything is doable with enough effort. One of the biggest reasons this doesn't typically happen in games (and that most games with "choices" are really just the illusion of choice) is that game developers don't want to spend an inordinate amount of resources and time dedicated to storylines that will only be experienced by only a few players.
So - Whiterun is in shambles because the Jarl's been killed. Now it's a ghost town for a few weeks before the vampires move in. Cool cool. Except now there is an entire branch of the game that has to be re-checked by QA to make sure there aren't any game breaking bugs or crashes that happen as a result of that massive change. And because it can happen at any point in the main story, it's got to be run through about 24 different checkpoints at various stages of story completion to again make sure that this doesn't cause some random variable to overflow or something to crash. Multiply this scenario out 10x or 100x depending on "what the player does next". Do you go in and kill the invading Vampires, or does this once-human city become a den of evil? Does having vampires in this city affect the Dawnguard storyline (it should) so again you have another branching narrative path that has to be run through QA.
It's also got to store the state of this change in memory, because like you said now maybe different NPCs have to react to you differently based on the outcome of this event (are you reviled by the townspeople, are you the new Jarl, were you popular but lost the election somehow?). This memory pointer has to follow your character for the remainder of the game in order for it to seem realistic. This pointer either has to be stored in local system memory (for fast access), local storage (possibly slow access), or server-side (even slower access and higher cost). System memory is extremely limited, especially on game consoles. A little more wiggle room on PC, but even still extremely limited when you're talking about the scope of the massive number of decision pointers you need to store in an open world game like this. And it's unrealistic to just do a Todd Howard and say "you just need to upgrade your desktop to 256GB of RAM in order to play this game". So - local storage. Cool, it's pretty plentiful (even not withstanding stuff like cloud save limitations). As a result, your save file grows up to be several GB in size. Problem is, now when the game needs this information it has to access the storage to get it. So if you're walking up to an NPC, and the game has to determine how they're going to respond to you (happy to see you, ready to murder you, many other potential emotional states in between), your console or PC has to read a several-gigabyte save file to determine the outcome of that interaction. This means freezing / stuttering - not good. So since space is a concern, you could store this value server-side and have the game access it over the internet instead. Your powerful data center servers could easily retrieve this information, but then you have to get it to the player. This means always-online, latency issues, etc. in addition to additional ongoing costs to support the game. Doable, sure - but not typically a good business decision.
And that's what this all comes down to - business decisions. I'm sure the people making Skyrim back in 2010 had a lot of really cool and wonderful ideas on how to expand the game to make it more realistic. Like being able to go back to the person who hired goons to kill you and threaten them - this is probably something that was realistically shopped by the devs but ended up on the cutting room floor because it would require too many system resources or business resources (dev, testing, QA) for something that only a percentage of people would do or see. As I said above, you could realistically program an AI / ML and data centers to handle these things for you but at a cost of hundreds (maybe thousands?) of dollars per player per month. Why do that, when you can give players a semi-realistic illusion of choice instead - and let their basic human instinct to use their imagination take over and do the heavy lifting for the rest?
I do agree that putting stuff like "a living, breathing world" in your marketing speak has always been 100% bullshit.