There's something of a divide among players, and to a lesser extent among games, between the sandbox style and the theme park style. Some people want to be led, and prefer theme parks; others, like myself, want to wander off, and prefer the sandbox style.
However, not all divides are created equal. This general point was brought up in regard to WildStar; it has a system of "player paths", like Settler and Explorer, which map to the Bartle types. However, using the Bartle types to classify players requires some fluidity; most players have a "primary" and a "secondary" Bartle type, and many(I don't know how many) want content from all four types. In WildStar, you pick a path. (Possibly one per character, it's still in development.)
Well, I'm used to looking for sandbox play in games, whether designed to be a sandbox or not. Many games that aren't primarily sandboxy still support sandbox play. But in reading about WildStar, it seems the devs were assuming they were exclusive — a divide with negative overlap, every bit of content being either sandbox, theme park, or failed. This was somewhat jarring. I still don't think I've fully thought it through, but here's a model which I think describes both play styles, and the nature of the overlap.
Extreme sandbox players don't want a story in focus, and less-extreme sandbox players are still less interested in a "foreground". One of the descriptions often given for sandbox play is "make your own story", and when you're making a heavy-sandbox game you need to focus more on providing tools to build with and a space that supports multiple stories. Support for sandbox play requires a "background", and letting the player leave your foreground behind in order to poke around and build on that background.
Similarly, theme park players are more interested in the foreground. For them, the background exists to support the foreground. If you present them with an interesting foreground, they will actively pursue it, and extreme theme park players will only explore the background when the foreground involves it, or when they can't find the foreground.
As a sandbox player, I don't normally think of what I do as "making stories"; however, that's more a difference of emphasis than one of type. And when you think of sandbox play that way, it becomes clear that many of the same tools needed by the sandbox player are also needed by the story developers. That is, "second-party stories" and "first-party stories" are built on the same base.
If your goal is to support both sandbox and theme park play styles, in the same way that most MMOs have some mix of all four Bartle types, it seems that the answer is to treat them as layers, the sandbox being a space which stories arc through. The classic quest model provides an easy way to do this, with stories built as quest chains, strung through a big procgen world. (I'm sure more modern tools can do it better.) Players are good at pursuing their own interests, enjoying the story or wandering off to enjoy the space.