A few thoughts:
First thought: Morrus defined what he meant by sandbox in the OP. The poll wasn't about the way the overall campaign is run, but rather about (essentially) wandering encounters on the world map. You may or may not have some sort of story arc or adventure path or etc in your overall campaign--what matters for the poll (as I read the OP) is what happens when you go to X encounter area on the map, regardless of when or why you are there.
Next thought: For many people the whole exploration experience some of us are talking about seems difficult to grok. You're probably going to have to come from the perspective that we are talking about something you
don't grok, and then try to learn what it is like you are taking a class learning some new scientific principles. Some of you are already doing this I'm sure, and I'm not trying to be pedantic here, but I think sometimes we all need to have that sort of thing pointed out (or at least it helps me): "Hey, new knowledge here! Student Mode activated." I'm not sure I'm the best person to explain it, because for me the principle is just a given (which in my experience from either side tends to make things difficult to explain), but I'll give it a whirl.
Part of the experience of playing D&D for some people is that a world exists in a non-variable initial data state, rather than having the initial data state for its areas influenced based on external information (like party composition) when first encountered. You know how in Skyrim the map is all created? It's like that. You know how in Skyrim monsters scale to your level? It's like
not that.
This allows a specific experience of exploring that data state as a separate entity, which isn't possible if that data state is influenced by your own data. It makes it more like visiting some place in the real world, and experiencing it. If I go to Switzerland as a tourist, I would expect that there are certain sites and restaurants in certain locations. If they started popping up based on my needs or expectations, it might be interesting at first but I'd start to think I'm crazy or in a reality simulation (cue obligatory link someone will post

), rather than being an actual tourist in Switzerland. I wouldn't feel like I'm getting the real experience of being in Switzerland (because I wouldn't be). When I'm playing in D&Dland, I want to get that real-feeling experience of being there and exploring!*
Why is that experience not attainable when a DM is just making it up as they go along? It's because the DM--whether conscious or not--will be adapting things to the PCs or their players. The DM already has that data, and it is going to influence their creative decision-making. They can consciously attempt to minimize that and get into a zone where they try to ignore the party for the creative endeavor, but that's an imperfect solution. The DM will also have a hard time remembering all of the data on the world that would flesh it out well--like when I make up NPC names during sessions rather than consulting a name generator (I do both) they all tend to follow certain conventions that make them sound like names I made up, while name generators give more variety. Same thing goes with types of foes present (oh, I totally forgot there are supposed to be a lot of bullywugs in this swamp...), treasure found (why is it always potions and sword, and never
horseshoes of the zephyr?), and even spontaneous events (another kidnapping? how come there is never an unexpected forgery fiasco?) This also means that what is found during exploration is dependent on the DM's current state of creativity, mood, what movie they watched last night, etc. A whole lot of variables other than the initial data state. Some DMs are better or worse at pulling this off, but it's always going to be a thing.
And the reason that thing matters is that, for this play principle, that initial data state is more interesting than the DM's variable-influenced data state. We want to explore the former, not the latter! (Same reason I like Elder Scrolls games but use mods to turn off the stupid scaled-opponents and treasures.)
That's really the principle at the core here:
some people find exploring the initial data state delightful in a way that exploring a data-state influences by other variables is not.
Now, as anyone involved in this conversation will be well aware of, the DM actually
cannot create the entire initial data state ahead of time. So does that mean this experience isn't even deliverable in the first place? Not exactly. There has been a solution for this since virtually the beginning of the game. Random tables that are part of the initial data state. That essentially totally solves that problem. The DM doesn't have to have notes saying that at hex A4 in the Darkwood there is a tribe of goblins, because he has a "Darkwood Encounters" table that is to be rolled on 3 times a day when people traverse the Darkwood, and has a 3.4% chance of generating a tribe of goblins. We random tables as covering all the bases, we now have an initial data state sufficient to create the desires exploration experience.
It's important here to re-iterate that these considerations
really do work for us to give us this experience. Since I'm taking a temporary "teacher mode", I'd say to the class something like. "Does that seem strange to you? Try to imagine why it might work that way for others? What's going on in their minds that causes that to work that way? Can you create that state in your own to 'see' it for yourself?"
Now, the astute will note that even that solution is imperfect, because you are unlikely to have sufficient tables to provide complete coverage for all of the empty spots in the initial data state. This is a valid concern regarding the information given so far. So we need to digress briefly into the DM's role in presenting this data state.
The DM's role in presenting this data state to facilitate the exploration experience is to present the information that already exists impartially, fill in the blank spots that have existing algorithms (random tables) by impartially applying those algorithms, and spontaneously create the needed additional data with an impartial focus on filling in that data state as it most likely would exist, regardless of the party encountering it.
That last part is about mindset. The DM isn't going to be perfect, but there is definitely a difference in effort and result between filling it what you think will be fun, interesting, or challenging for the party, and filling in what makes the most sense for the world without conscious consideration to the party. By following these steps you minimize the DMs unintentional and unconscious adaptations to only affecting the limited blank areas in the initial data set.
These three elements flow together to really enable this delightful experience of exploring an initial data state uninfluenced by party or other considerations.
Now, it's also worth emphasizing that this is about establishing the explorable world. This doesn't mean that you can't set adventures in it customized to the party, or otherwise create customized content. What is vital here is that this is a separate thing you are doing from creating the world's initial data state. It's part of the campaign (which itself should be thematically compatible with the world's initial data state, of course). It's like adding expansions Skyrim. They don't invalidate what came before, they just add new data. You might (actual example) place the Forge of Fury adventure in the Pomarj, and decide that in the aftermath of the Greyhawk wars, the Principality of Ulek is launching a counter invasion to attempt to reclaim their land from the Pomarj, which means the normal encounter tables are replaced with new random encounter tables that are more appropriate to the war going on. You might also decide that there is an NPC adventuring party from the Wild Coast down in the nearby village where the PCs first arrive at, because you had some fun ideas for that adventuring party. The initial data state is being expanded with new data chosen for either the campaign (in the case of adding the adventure) or for the world (in the case of the counter-invasion). This doesn't change the order of operations for the DM in play at all, they just have an updated set of initial data they are dealing with. This also doesn't mean that you can't insert fun things into the data set spontaneously on the fly. This is one of the things that a DM can do that a computer game can't. It is important that inserting those fun things follow certain discrete principles.
Essentially, when you insert situationally customized things into the experience spontaneously (rather than creating them at some point as an expansion to the world or campaign or generating them with the random tables included in the initial data set, or making things up to best approximate what makes the most sense for that initial data set), it is like you are playing a PC**. These new things you create in that way are bounded by the data in the same way that the players' characters are. You can spontaneously plop down an NPC that you think would be interesting, but you can't rewrite the world or ignore the results of random rolls, because that would be influencing the initial data set. This is the most subtle distinction, but it is real. The DM treats the initial data set (including later creative expansions) as authoritative, and works completely within the boundaries of that state during play, exactly like player characters.
By doing so, the DM is enabled to also explore the world in a way similar to the way the players are (though to a lesser extent).
While it might seem like there are a lot of fiddly details to this (and generally we don't think through how this all works the way I did today), these are the underlying principles at work, and they really do work to create that awesome exploration experience some of us love so much in our D&D.
*One might hire a tour guide in Switzerland to take me to a curated set of destinations customized for my interests (or the expected interests of tourists) which is fine and is analogous to a pre-made adventure in D&D. But if I decide to ditch the tour guide and explore, the world is going to be there regardless and I get to explore it. The same experience is desirable in D&Dland.
**As is fairly obvious, the PCs in such a game generally lack narrative control outside of their individual choices of what to do, since that's another way to interfere with the exploration experience. If I'm just declaring that a certain site will exist when I turn the corner in Switzerland, it's no better than a cosmic DM doing so.