I'm not doubting that for some people it is a gap.
What I'm and I assume others on this thread are arguing is that:
1) this work to bridge the gap in some people's mind I believe is real and I understand how that could prevent people from liking 4e. if you can't approach 4e with certain mental frameworks it does breaks down. However...
2) there is a mental framework that works and makes everything pretty coherent. it is not useful to illustrate a bunch of ways the system breaks down when approaching 4e from a mental framework that leads to nonsense. EVEN if the books are confusing, non committal, or even intentionally lead you to a poor mental framework (which I don't think is true btw). At this point, who cares? Use the mental framework that makes things make sense, or if that is too much cognitive work to be fun then move on. But continuing to state the implications of approaching 4e with a mental framework that you know will lead to nonsense when there is a framework that won't? I don't see the point.
It's a continual theme in these 4e discussions, of which the meaning of hit points and healing is just one example.
Nature of minions -- things get nonsensical if you apply a simulationist framework where you expect minions and all stat blocks to be an actual thing in the world instead of a mechanic to represent relative interaction with PC characters of X level. Actually this includes another example of HP in 4e best represented as the amount of effort needed to be "taken out" of a scene. If I remember minions can't take damage on a "miss" (another poorly labeled and explained mechanic -- but it works in the right mental framework!)
DC by level -- things get nonsensical if you apply an interpretation where everything scales with level around you regardless of the in game fiction. I've seen people argue that regular locks in farmhouses would be Level 25 DC if encountered by a Level 25 party? Why interpret the system this way when another framework leads to coherence -- that Level DC guides are meant to give you a value for level appropriate challenges and those level appropriate challenges should be in fiction different very different for Level 1 characters and Level 25 characters. And that 4e is not designed to mechanically model rolling dice to resolve Level 25 characters trying to get into a regular farmhouse. If you did have a PC roll dice, it should be against whatever the regular farmhouse lock DC would be though -- say Level 1 or 2 DCs -- auto success. 4e is primarily designed to model and resolve challenges and encounters that are more or less near Level (within +/-X), and assumes the heroes are seeking out those appropriate challenges, which will change in fiction as they progress in level and Tier.
etc.
Presuming I'm reading your post right, you're essentially asking "you already know that 4E doesn't work with your preferred style of play, so why are you critiquing it?"
The short answer is because I want to better understand how it's different from not only my preferred style of play, but also from the other iterations of D&D which better dovetail with said play-style.
The longer answer is that we can all perceive that 4E is different from its predecessor editions, and given that I find D&D and its history endlessly fascinating, I want to analyze those differences. Moreover, I want to do so in a public venue, where others can add their thoughts and insights. What goals were set for 4E, and how did it attempt to achieve them? To what extent were they achieved, and how artfully (or lacking in artfulness)? In what manner were these different from prior editions? All of these are worthwhile questions, and deserve to be brought up, even if the critiques don't paint a flattering picture of 4E.
I noted in the OP that 4E had the shortest shelf-life of any modern edition (where "modern" means "debuted as of the year 2000 or later"), which is the most non-judgmental way I could come up with to say that a significant portion of the D&D community rejected it. Why? What about it caused that reaction?
We can talk about a lot of factors external to the nature of the 4E rules and setting in that regard, to be sure. The GSL. The DDI. The marketing. The pulling of older-edition PDFs (though I need to double-check the timeline there). And quite a few others. But if we make what I think is the non-controversial assertion that a not-insignificant part of the reason why so many in the D&D community couldn't countenance 4E was because of the structure of the game engine (though the changes to the lore was also part of it), then that justifies taking a look at those aspects of the game itself, both in terms of what they do and how they compare to previous editions (and, by extension, the presumptions that previous editions inculcated in their fans as to what exactly D&D is "supposed" to be).
Jon Peterson wrote an entire book about the history of attempts to define exactly what role-playing games are (that being
The Elusive Shift), and the entire reason why he had enough material to make a book about it was because we've barely been able to scratch that surface, even after five decades of community engagement and development. The
threefold model.
GNS theory. Trying to parse the difference(s) between a role-playing game and a
storytelling game. And quite a few more. In that regard, we can take a narrower focus, and try and figure out what D&D "is" and how its various editions play into that paradigm, both in terms of where they're the same and where they differ.
4E is no exception in that regard, nor should it be.