I think that is in part because with a lack of challenges it becomes hard to highlight the difference. We seem to have a deep struggle in this thread to even define what is and what isn't exploration and why that is. Now, you may have an answer that seems obvious to you, but others of us are seeing it from a different angle that makes your answer not seem 100% accurate.
Is describing a location important? Yes, it could even be considered the most important thing in the game, but that is because we can't do anything without describing it, and therefore description is a part of every single pillar. Which makes it difficult to imagine that's what was intended. Setting it up so one pillar is the bedrock of the other two isn't having three pillars. So, for a lot of us, we go forward with the idea that this isn't the case. That description =/= exploration.
So, I don't think it is that people think non-challenge exploration isn't "important" to a smooth running of the game, as much as they are saying that it is so integral to the game that it can't be a pillar like the other two. You can't interact with the gameworld without moving through it, so the "exploration pillar" can't default to being that, because that is such a bedrock element that you can't seperate it from any other portion of the game. Which means "exploration" must be something else, something smaller.
Or we have to allow the pillars to overlap, and assume they rather often do.
I certainly don't see them as being completely isolated; they're more like three partly-overlapping circles on a Venn diagram.
See, this is a weird non-starter for me. Re-rolls make sense. I'm going to switch examples to highlight this, but I'll try and bring it back to exploration.
If I try to break down a door, and I fail in real life, then I can always try again. I can try again in the exact same manner, and there is a god chance that, given enough repeats, the door will wear down. However, by not allowing re-rolls it feels like I get a single chance to break it down, and if I fail it becomes an impenetrable force construct, locked into reality and immovable. You can say "you put in your best effort" but I know that isn't true, because I know my best effort would break down the door.
Interesting example, and a good one; in that in my game whenever you try to break down a door I'll give the door a saving throw. If you succeed by a lot in your own attempt, door's broken no matter what. If you succeed only by a little*, or fail**, the door's save will sometimes tell you whether it's worth trying again. In broader terms, a poor save by the door indiates it's been weakened by your attempt; this is a material change in the situation and thus if you try again you'll get another roll, likely modified in your favour.
In searching, the only ways to effect a material change are to either have someone else do the searching or to change your own approach.
* - here, the door's broken but a secondary effort might be required to get through e.g. moving the remains of the broken door out of the way; all this costs is a bit of time and maybe more noise.
** - if you fail terribly i.e. roll a 1 then I'll skip the door's save and there'll be a secondary roll to see if you hurt yourself.
It ends up feeling like the DC changes. As though it goes from whatever value to infinite after a single attempt, which is very jarring to my verisimilitude. And going back over a paper or a book or a searched room and finding something that you missed before happens all the time in real life. It makes sense.
To a point, I agree; but I also want to get away from two things: auto-success (and auto-failure) where such is in doubt, and lots of re-rolls.
Now, I get why you don't like re-rolls, because what they mean is that given a non-threatening environment, the players will always eventually succeed. And I think that is why I prefer sometimes to take a roll that failed, and say that instead it succeeded, it just took longer. It is the idea of failing forward, but I think I want to evolve that concept a bit. Not right now, but ideas are percolating as I'm writing.
I'm not much of a fan of fail-forward as it's been presented, mostly because it often seems like the intent is to turn a failure into a success-with-complications. To me, a fail's a fail; success-with-complications can come in on a narrowy-successful roll, rather than a failed one.
What if failing a roll, not catastrophically, but just by a bit is the driver of that Doom Pool idea?
Not familiar with Doom Pool. Readers' Digest explanation, please?
I struggle with the exact cut-off point, but looking at Xanathar's tool rules and everything else, I think I lean far more to the Eberron Model. By level 1 you are already highly trained, and by level 3 you are exceptional.
That sounds very much like the 4e approach: you're already heroes before you even start adventuring.
However, I also tend to make a lot of other people exceptional too. Your blacksmith PC is as good as any highly-trained blacksmith, but the City Watch in the Capital are all likely level 3 fighters, because they are just that good.
Kind of like a rising-tide-lifts-all-boats idea. Got it.
I do a bit of the same thing myself, but I guess I start from a lower tideline. A 1st-level adventurer isn't much removed from a commoner (I've got a 0th level in between), while a 3rd-level adventurer is - while certainly better - still rather mortal.
At the other end, there's always a bigger fish.
IT causes issues, the game isn't set up well for how we balance the power of PCs/NPCs/and monsters in the world, but there has to be a middle ground.
I think there's an opening to flatten the power curve significantly by making everyone except commoners less powerful in general, starting right at 1st level (or 1 HD for monsters) by making those be closer to commoners and then scaling back the powers gained through levelling.
The problem is that to do this in the current 1-20 environment would necessitate "dead levels", which while being fine with me tend to generate howls of complaint from others. So, the answer might be to reduce the number of levels - sure, design from 1-20 but make 1-9 or 1-12 the playable range (and thus, those are the only levels shown in the PH) with harsh warnings for DMs that going beyond this will cause things to wobble; the higher levels are presented in the DMG largely for purposes of world, monster, and opponent design.
shrug I have never had a party not roll with advantage. They always use the help action on every check they can. And a lot of abilities exist to boost skills, and they all tend to stack.
Which makes it difficult to find appropriate challenges. I think 5e does better, but it isn't perfect.
Quick and dirty houserule idea: disallow some things from stacking.