Recognizing "pillars" of the game can be a useful tool, but like all tools it can be abused. Here's how I think they should be approached.
1) As a descriptive model relating how the game is played to the "reality" of the game's world.
2) Like a basis vector in linear algebra. This means that we recognize that not all elements of the game can necessarily be broken down neatly into one pillar or the other, but to a large degree all elements of the game can be described as some combination of them. Moreover, the set of basis vectors is not necessarily unique, so that one can imagine "relabeling" the pillars and getting a new set of pillars that still describes the same basic game. Sometimes shifting the "pillars" can make situations otherwise described by weird combinations more intuitive.
3) Recognize that "All models are wrong, but some are useful." - after George Box. An open-ended game like an RPG is sufficiently complex that no playable model can completely describe it. In the end we mostly want the pillars to help make better games, not be the ultimate theory of game design. This is also a good reason to avoid making the pillars proscriptive, since doing so inevitably highlights all the places where the model doesn't quite work.
In general, I believe the hypothetical "perfect system" maximizes game immersion (however one wants to define that for a particular game -- one size does not fit all) with mechanics that stay out of the way when necessary, yet are interesting when pondered. Games that are "easy to learn, difficult to master" often approach the mechanical goal, and games where the rules are unobtrusive yet expressive generally support the immersion ones. Marrying the immersion with rules that meet this characteristic is probably the nirvana of game design.
In design it is relatively easier to pursue the immersive goal or the mechanics goal separately, so to achieve both in the final product almost certainly requires iteration. Some people start with an idea for immersion (e.g. "a virtuous soldier sent by divine agents") and search for mechanics to express this idea. Others start with some cool mechanics ("two dice show the same value") and then search for story elements that might sensibly represent that mechanic.* Then back and forth, back and forth, hopefully to preserve or create the fundamental coolness of both even as they undergo changes. How can the pillars support that process? By helping the designer know what questions to ask in order to see what effect any given set of changes has.
Consider a classic utility spell with a lot of personality like rope trick. The idea of a character creating a small interdimensional space with a fairly peculiar interaction outside that space is very rich, and as a concept apart from mechanics, just "something a wizard can do", is bursting with possibility. It's also bursting with the possibility to dismantle an encounter or adventure, so the mechanics need to be considered carefully. Considering the mechanics and the spell's concept in like of pillars of the game can be a framework for guiding its evolution. It can help determine whether some use is just so good that it needs to be disallowed specifically (usually an inelegant solution), or whether a more general change will indirectly reduce the chance of abuse while also maintaining its core functionality. And so on.
In other words, pillars can be a pragmatic way to examine how well some rules are meshing with the game, with more specificity than simply asking "how can this break." It can force the designer to think less abstractly, and more like a player or a DM with a goal in some scenario. Finally, it can help the designer make informed decisions about whether the concept or mechanics should be narrowed because, in some implementation, they simply don't mesh. Generally speaking, game designers don't want to design a game with all sorts of ugly seams where the rules change in order to make the game work, but it's good to know where having a seam is likely to be, on the whole, better than the alternative. Some seams we generally accept as a community (e.g. the in-combat/out-of-combat distinction) and others are more controversial (e.g. the actuality and/or perception of 4e attack powers having very little interaction with the world outside of combat).
Overall, I'm very positive about recognizing pillars, and am not even that particular about the specific ones that are identified unless they are really terrible. However, my enthusiasm is muted as the guidelines above are more violated. For example, "siloing" feats along the lines of the pillars (as per the recent WotC blog and thread) is generally distasteful to me because it makes the pillars proscriptive and makes some character abilities that should naturally involve multiple pillars awkward to write, and highlights the deficiencies when that awkward writing isn't overcome. I consider it a seam, more or less. That's a topic where I'd want to carefully iterate possible design to see if siloing is necessary, and if so then to integrate it in a way that minimizes schizophrenia in character abilities. Having the concept of pillars can aid that process, and I consider that a good thing even if the final execution doesn't fully satisfy me.
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*I know this method is sometimes frowned upon, especially when it results in creating an option that seems to exist solely for "symmetry" with other game elements. It gets a bad rap, in my opinion -- if one has cool mechanics that don't mesh well with the story/mythos/whatever, one should drop the mechanics or keep searching for an inspiring fit, not malign the starting point for the idea. It's a matter of discipline. As game designers it is easy to fall in love with our own mechanics and hurt the game, like a movie director unwilling to cut a good scene that nonetheless destroys the flow of a film. Likewise, people that start with an idea that strikes them as immersive can also hurt the game by failing to find fitting mechanics to express their idea, but keeping it in anyway.
