IMO not that important with most games and here is a few examples why
Your father has died
You are starting a new school/college/university
You have not seen your mother/cousin/ex-wife/sister/daughter etc..... for years
You have just moved to a new town/city
From then on you fuck everything in sight, but only after numerous hand jobs and blow jobs.
So, you're saying that's the games you like because story doesn't matter to you? I have to ask because it was unclear whether you were stating your preference (as the OP and thread title ask "How important ...
to you"), or attempting to criticise the mass of games that don't do a good job, and
criticism tends to imply that you do think it is important, personally.
Now sure, there are lots of games that don't have great story, or plot, or writing, or in many cases, even such basics of writing as spelling and grammar. That's quite normal. The vast majority of people aren't very talented in a wide variety of skills, so that most people are not at the level of even a poor professional writer is really no more surprising than that most people are not at the performance level of a poor professional sportsman, or a poor professional chef, or a poor professional electrician.
Then of course comes what is known as
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. This is simply the realization that the skills it takes to accurately evaluate the performance of a task, are the same as the skills to actually perform the task. Someone who can't write is, by the exact same limitation of talent and understanding, utterly unable to detect just how badly they suck at writing. The upshot is that the worse someone actually is at a thing, the more they over-rate their own ability in it.
Research has consistently shown that when you ask people to rate themselves against 'the masses', people tend to assume themselves to be better than average. Such that the average in any such sample all believe themselves to be better than average...
The interesting flip-side is that people who really know a topic, have often studied the works of masters. So here, instead of a guess based on an unobserved 'average', these people are aware of the giants in whatever field, the best of the best, and compare themselves (usually unfavourably) to those.
It's that old thing that those who don't know anything, literally don't know how much they don't know. They are pretty much completely unaware of their lack of ability or knowledge. The more you study and master a field of knowledge, the more you realise is still unknown, and may never be discovered. So the truly talented in any field tend to under-rate themselves - partly because they are aware of so much they don't know, and partly by comparing themselves to the masters of the field from whom they have learned.
What this all means is that the less you know, the more you think you know. While the more you know, the less you think you know compared to all that is out there that you wish to know.
That and if you ask everyone to rate their taste in games, they will
all tend to believe they are better than average.