Does the main story matter in open world games?

[Mnementh]

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.