There needs to be a main story that ties everything together and enables everything to come to an end eventually. I'm not going to play a game just for the heck of it, it needs an arc that has a beginning and an end. I usually complete all side quests before finishing the main story, but I would never buy a game that was all side quests and no actual backbone. Side quests tend to be repetitive and of little consequence. The worst of all are endlessly and randomly created dungeons. What's the point of those? I like to do things once, have an impact on the game world and then move on.

If you don't care about stories in open world games then that's fine, the important thing is that you are immersed in the game. For me, the story is always important and its disappointing if the quality of the storyline does not hold up to the quality of the gameplay. That is not to say that I cannot enjoy a game if the storyline is mediocre or bad, being a gamer you kinda get used to that, but I always prefer having a great story + great gameplay over just having great gameplay.

Story always matter. It gives the game a purpose.

yes

i play most games because of the story.

story gives the game and struggle to play the game a meaning and an aim and an end to it

A big open world ready for you to explore so you can write your own history. That's the kind of open world experience I want from a game.

Sadly I think there is no game out there that accomplishes that since they all have a main story that detracts from the "create your own history" theme I want.

But to answer your question. I do the main quest as soon as possible to get rid of that nuisance. Then I do whatever I want. But I get bored very fast so I don't play those kind of games anymore. If someday open world games get to the point where you can explore the game and just create your own adventure, that's when I'll jump back to them.

Always. Story is like one of the most important things in games imo.

GTA can do this both and i hope FFXV will do this on the next level (but i doubt it will be full sandbox games like GTA). And I believe XCX will not be story focus like traditional RPG does (it's more like Monster Hunter games with story and plot added on the games). From the trailer and early footage i only see one big cities and quest related games and by completing some quest the stories will advance automatically. Unlike FF XV where exploring new cities is part of the games.

While a good storyline is always welcome I have to say: if you want an intriguing storyline, an open-world-game somewhat beats the purpose, because in an open-world you always can stray away from the main path to do side-quests for forever. So if you have some storyline that says the world is endangered or something like this and you have to save it, it diminishes the sotry if you start doing open-world stuff and shoving saving the world aside - because the world will not end until the final boss-fight anyway. So an open-world game meshes better with a story, that only gives hooks to open up and explore new regions but allows the character to do other stuff.

In most open world games I've found the smaller side story's/missions to often be more memorable than the main story.
Let's face it most games "main story" is generally just save the world and beat the bad people. Side quests can be anything

Yeah why not, i can respect any game with a good story. Shadow of Memories for example was the complete opposite of open world and that game turned out to be great for me because of the story.