I think you could. A big sandbox or dungeon. Make no story but set the scene and what the NPCs want and will do without interference.
I think it's harder to make, harder to run, and probably harder to sell.
I also have a "take", I think most players want a story. Or they want to play that story, which isn't the same as passively watching a TV show or reading a book. Definitely more "railroady" than an open sandbox or variant path dungeon.
One of my pleasures over the last four years is discovering the current state of computer games. And you can learn a lot about potential paths for storytelling in D&D by looking at them.
So, you have very linear storylines like
The Last of Us. Most of the side content there is "can I find a collectible". The storyline has no choice points, and the game is in how you overcome challenges. Oh, the number of times Joel or Ellie died when I played!
Incredibly linear, and yet still incredibly popular. Because the writing, story and performances elevate it.
Moving along the scale, we get to experiences like
Cyberpunk 2077 and
Assassin's Creed: Odyssey. The core of these games are still linear, but there is more of a variation on how they're approached. You can change the order in which you do missions, there's a lot of side content, and your choices can resonate later. Not to an incredible degree, but they do occur. And obviously,
Baldur's Gate 3 takes the concept of choice and consequence even further, while still (overall) having a central narrative.
And then you get
Skyrim, where I'd say most players completely ignore the central narrative and just go off and do the handcrafted little quests, as it moves about as far towards a sandbox as you can get while still having a sense of storytelling.
One of the interesting things about these latter games is how they handle level gain: and it's through dynamically scaled encounters. (Cyberpunk added that in the 2.0 update). It's one of the ongoing issues for D&D with big sandbox adventures: players very quickly level past content.
Consider
Rime of the Frostmaiden, where there are all these low-level missions in the first chapter, but it doesn't take very long before the players have completed a handful, and the rest are no longer useable as written.
Cheers,
Merric