Hear me out first.

This is not about if a story adds to a game or that a good story is always important. This is about what people want out of the game and what they focus on. Since open world games pretty much do everything possible to draw your focus away from the main story.

Also "main story" does not include the setting, characters and world which obviously is one of the most important things in such a game. It's just about the main story quest line.

I don't really give a shit about the main story in any open world game. Simply because I don't play those games for any kind of story. I play them to explore an open world. Discovering nice places, tiny little side quests which add to the world, beefing up my equipment and becoming stronger and finding the rarest items in the world.

I played Oblivion for multiple times and hundreds of hours without even touching the main story line. That's not because it is particularly bad or boring but just because it's just not that important for me. Oblivion is qactually a really great example for a proper open world game. Because most other open world games force you to advance the main plot just so you can explore more or get better stuff as an arbitrary wall.

So what do you think?

Most of the time in my experience, the open-world games have the tendency to just pause the story during a quest to the point where I forget so I have to say meh not really.

I mean games like Majora's Mask's main story is meh but I hear the side quests are the real meat of the game.

It does if it has a great story. I mean sure you can get lost in all the side quests but there is no reason to not have a great story experience and get lost in the side quests in open world games but I do feel like that the story in a lot of open world games isn't good enough to keep me interested in the story.

If an open world game can tell a story, then great, but it's generally something I don't care too much about in that particular genre.

Actually, Majora's Mask's main story gives the whole game the theme and depth it's been known for.  For instance, because there is death looming over the people of Termina, there is a heightened sense to finish the game quickly or at least finish the objective of the portion that the game is in. 

To answer the question, some games need story(in my opinion the better ones), some games is just the hub.

I hold the story in very high regards in my games so yes it matters to me.

It depends on the game. But a game like GTA and Skyrim needs to have a hook for me to care about doing any of the open world stuff.

If the story isn't good, then it has to have really good stuff to do in between story sequences. Very compelling gameplay or environments fun to navigate, like the inFamous series. Stories are average at best in those (except for the first game which I thought had nice plot twists), but the gameplay and traversal elements make the games very fun to play.

But usually I eventually lose interest if I don't care about the story and its characters.

I think it depends on the game, sometimes the core story is what's important and others it's about having a huge range of tasks that is important, or just the general massive exploration and discovering all the intricate complexity of the game.

IMO provided the developers have reason to make a game open world, it works for what that game and is fun to play around in then I don't mind either way.
If I have to play a certain part of a story to open up a new section of the game's world that's cool, an aimless experience can get boring because it can become repetitive.

But is there really a need for an overarching plot if you have just random fun in the world?

That's game dependent... For games like Skyrim and Saints Row, not really but for games like XCX and FFXV, yes