RC, would you have a problem if story instead was defined as:
"Game events that everyone at the table decided the PC's will experience although the exact details are undecided."
I would not qualify that as a good working definition of a sandbox.
Things you either cannot do or are damnably difficult to do with a sandbox campaign:
Survival horror. Why not? Set the sandbox after the collapse of civilization. Sprinkle with infectious zombies. The best treasure you can find are a few shotgun shells or a flashlight.
High fantasy, particularly quest fantasy. Why not? As has already been noted, LotR could have been played as a sandbox. If the players opt in to the quest, there is your quest fantasy.
Campaigns where the PC's are integral to the campaign. This is a bizarre thing to think you cannot do in a sandbox. Whyever couldn't you play a fighter who has control of the lands all about? After all, isn't that what the original game was pointed toward? If you wanted to play Battlestar Galactica with the players taking the roles of the positions (not necessarily the characters) of Admiral, CAG, President etc., why not? Sandbox doesn't affect who you are -- merely what you can do.
Campaigns where you have a present chain of command. Why not? I have played in a sandbox based off Star Trek TOS. The chain of command is part of the sandbox. You can go against the chain of command. Kirk did.
Spy campaigns (after all, Bond doesn't wander around looking for bad guys, he goes on missions). Again, so? And, your knowledge of Bond is weak, my friend. He does indeed wander around looking for bad guys, both in the movies and books.
Campaigns focused on single (or very small numbers) of themes. Why not? All one has to do is devise areas, characters, and other game elements based on those themes.
Before the wailing and gnashing of teeth. Yes, I know you can work around those campaigns in some fashion. But, it's going to be very difficult and possibly not worth the effort.
It will not be difficult at all. Not even remotely.
Any halfway decent GM could pull off any of these sandboxes with no more effort than a typical D&D sandbox -- in some cases, quite a bit less -- and could do so with very satisfying results. Are you claiming that you would find any of these difficult?
----
I do admit that, near the end there, I was just skimming your posts. Once you started telling me what I was saying (without any apparent comprehension on your part) and started quoting me saying X when what you quoted said Y, I began to think I was wasting my time giving your posts any real consideration.
That being true, I should simply have ignored them.
My apologies.
RC
EDIT: Going back and re-reading your post, though, I can see why I misunderstood. Because you didn't identify which style you were talking about clearly in the bit I quoted, I thought you were saying more of what you were saying upthread.....i.e., how one cannot have any depth, etc., etc. with a sandbox.
And you still haven't answered many of the questions asked of you.
The idea that the players choose the world when they create their characters begs the question, "What happens when a PC dies?" Must the players also be given plot protection, further eroding the meaningfulness of their choices, or must the world be changed with each new PC? What if Cousin Susie joins the group? Do we change the world again? If not, how, oh how, is she going to achieve any depth in her play experience?
How many players do you have?
How many players did you have while running the WLD (which is, essentially, a limited sandbox)? How did you keep them engaged? Are you ever going to answer any of these questions?