(1) Notice that I didn't say that exploration is a problem. I said that I think it is obvious how the following might be a problem: a player who is hoping to change the fiction, by way of an action declaration for his/her PC, discovers - in virtue of how the GM approaches adjudication that s/he is really exploring the fiction.
The risk of such a problem is not obviated by pointing out that exploration is a "key pillar" of the game.
The risk? No. That it's a problem at all? Yes.
Here's a trite illustration of the point: drinking water is a key pillar of human existence. But it might be a problem if every time you go to eat some food, or drink some beer, or . . ., you find yourself drinking water instead.
Not quite. Closer to the point here would be a situation where you go to drink some water and find it's tainted, or is in fact vodka or gin.
Here's a slightly less trite illustration: if a player is setting out to do something in a different "pillar", and discovers by way of unanticipated GM adjudication that s/he is really exploring, then s/he might feel surprised or even disappointed.
As would the PC; and
this is perfectly fine. Same way I'd feel if I took a swig of water only to find I'd just downed a mouthful of Gilbey's Finest London Dry: I don't like gin, and so I'd be both surprised and disappointed...and probably a bit annoyed too.
What was my mistake? Not sniffing the "water" first...i.e. not fully enough exploring my surroundings before interacting with them.
(2) The idea of pillars of exploration, combat and social is actually distinctive to some versions of D&D.
It doesn't generalise to Traveller, in which making a FTL jump is a moment of action resolution that is neither fighting nor talking but is not exploration. It requires various rolls to avoid misjump, drive failure and the like.
Regardless, after the jump you're going to be somewhere you weren't before - a place which you either know through previous exploration or don't know and thus will probably want to explore - even if such exploration consists only of looking out the window (and-or checking the sensors) to see what's around you before jumping again to somewhere else.
It doesn't generalise to Burning Wheel, in which chasing someone or buying something can be a moment of action resolution no different in basic mechanical structure from fighting or talking, but obviously neither.
Actively chasing someone usually falls under combat; surreptitiously following someone would be more in the exploration side. Buying something falls under social. That the game has specific mechanics for these things doesn't deny the pillars are present.
Come to think of it, I wonder if you can name anything a PC might do or try to do within the fiction of an RPG that doesn't fall under one or more of the four pillars including downtime?
It doesn't generalise to 4e D&D, which has two basic pillars - combat and non-combat (skill challenges) - and the latter can be used to adjudicate social interaction, crossing a desert, altering or dispelling a magical phenomenon, etc.
4e does kinda take two pillars and shove 'em into one, but when looked at more closely each thing within the one can be broken out. Social interaction = social (obviously!); crossing a desert = exploration. Altering or dispelling a magical phenomenon = some situationally-dependent mix of combat and exploration if done under duress, and quite possibly downtime if done in the safety of town.
This all rests on very strong assumptions about how RPGing works. I'm sure they're true for how you play D&D. They're clearly not true for (say) Dungeon World played by the book.
To elaborate: the most common way that the players in my games learn the parameters of their in-fiction surrounding is by asking and being told.
This is likely true almost universally, as far as it goes. But it's only half the picture...
That is, they don't declare actions with the intention of having the outcome being narration of fiction; they (as players, not as their PCs) ask me and I tell them.
So they never declare any action on the basis of "let's try this and see if it works"? No trial-and-error, intentional or otherwise?
The other half of the picture is, of course, hidden information that the PCs (and thus players) can't know until they discover it, sometimes the hard way. The no-teleport zone would be like this, as would be the gin-water. Or do you flat-out tell them if they ask (and even if they don't?) it's a no-fly zone even if the PCs have no way of knowing?
Sometimes this has collaborative dimensions, in the sense that together we establish the parameters of the fiction.
In our last Traveller session, for instance, through asking and telling and working together we established fiction about Imperial Marines insignia, the player of an ex-Marine established some details about salutes and signals, we referred to rulebooks to ascertain exactly how battle dress (a type of powered armour works), I described to the players the existence of force-field type technology that is used to maintain heat in open-air areas on the icy-cold world the PCs are currently on, etc. None of this took the form of exploration in the D&D sense of delcaring actions like "I prod it with a 10' pole". It was all about establising and sharing backstory and establishing clear framing of current situations.
No, but it all fell under the exploration pillar in terms of learning about the setting and how things work there.
Another way the fiction in my games is established is as the outcome of action declarations. In a BW session, this was how it was established that a sick-room contained a chamber pot (a player made a successful Perception check to notice a vessel in the room). In a Cortex+ Heroic session, this was how it was established that some runic inscriptions described the dungeon layout (because a player declared an action to eliminate his PC's Lost in the Dungeon complication, using the Runic Inscrptions Scene Distinction as a component of his dice pool for this action).
Yet another way is because players make checks that oblige me to make up new fiction. This is a part of Dungeon World - you'll recall the discussions upthread of the Discern Realities and Spout Lore moves, which - if successful - oblige the GM to provide the player with certain bits of information:
Spout Lore
When you consult your accumulated knowledge about something, roll+Int. ✴On a 10+, the GM will tell you something interesting and useful about the subject relevant to your situation. ✴On a 7–9, the GM will only tell you something interesting—it’s on you to make it useful.
Discern Realities
When you closely study a situation or person, roll+Wis. ✴On a 10+, ask the GM 3 questions from the list below. ✴On a 7–9, ask 1. Either way, take +1 forward when acting on the answers.
• What happened here recently?
• What is about to happen?
• What should I be on the lookout for?
• What here is useful or valuable to me?
• Who’s really in control here?
• What here is not what it appears to be?
It's taken for granted in DW that that information won't have been pre-established - the GM is expected to make it up on the spot, building on what has gone before and the current dynamic of play (including previous "soft moves" made by the GM) - [MENTION=6696971]Manbearcat[/MENTION] and [MENTION=16814]Ovinomancer[/MENTION] have discussed the details of this technique upthread.
Those are still all exploration, regardless of the mechanics used. D&D Bards have a Legend Lore ability that sounds quite similar to the Spout Lore noted above; and well over 95% of the time when a Bard in my game succeeds with Legend Lore I'm immediately making stuff up on the fly (they chuck LL at some of the strangest things

) so I can narrate the information obtained.
Information gathering of any kind is exploration. Occasionally combat might enter into it (see: torture), and far more often social enters into it (when you get the info from another person or entity in the fiction), but it's always exploration at the root.
Similar things happen in my Traveller game, though in Classic Traveller it is mostly less formally structured.
In the first session, after the PCs had been briefed by their patron, one of the players was suspicious because the whole thing didn't make much sense:
...
For the character in the fiction, of course that's all about figuring out what is going on. But for the player, given that I am approaching my Traveller game in a DW-type spirit rather than a "secret backstory" spirit, it's about using action declarations to force the referee to provide more detail in the framing, thus providing the player with more fictional "levers" on which to hang action declarations.
And notice that this is the player doing this. (Just as, in DW, it is a player who triggers Discern Realities or Spout Lore.) Which relates back to the first part of my reply - my response as referee conformed to the players intentions in declaring the action (ie forcing the GM to enrich the framing to provide more fictional levers).
And in these instances the player is simply trying to mirror the character, which is great.
You aren't always going to describe every last little feature of a scene and nor is anyone else. Players can (1) ask for more (or more specific) info, or they can (2) declare actions that'll get them the info. Either way, for better or worse they should end up learning more; and in many cases it'll take a bit of both (1) and (2) to fully suss out a scene or situation.
The difference with (2) here is that it might draw out information that simple observation (1) can't get - as in the no-fly zone or the gin-water. For example asking you to give a more detailed description of the items on the desk will get me that, and I can in theory drill down (within reason, of course) until I'm satisfied; but it'll still take the action declaration of "I cast Detect Magic" to pull that one of the four otherwise ordinary-looking dust-covered quills on the desk is enchanted.