My experience was very different. Reading the 4e Monster Manuals and players' manuals (not the general rules, but the power lists) makes me want to see these things in play (and to imagine what might happen in the course of such play).
That's not really that different from my experience. I remember my old group going through the PH1 for the first time, and being excited by what the powers could do - particularly fighter and rogue powers, for obvious reasons. A bunch of hobbyist can look through even a dry, technical manual and have those kinds of reactions.
And, sure, there was flavor stuff in 4e. It drops hints about Nerath and Arkhosia and so forth. It has sidebars about what the power sources represent and stuff like that. On balance, though, it didn't compromise being a decent reference book to be a better read.
It's not the same as reading a story, obviously. But I don't really read RPG books for story.
I appreciated the readability approach in Storyteller, even as I was frustrated by the lack of adequate indexes and crunch. I liked having good rules I could fairly easily look up in 4e - and the best of the bad lot of Essentials core books was the pure-reference Compendium - but I didn't ever read /everything/ in any of them, because they don't have that readability. Both styles are perfectly valid and have their good and bad qualities.
The Essentials verbiage, on the other hand, I find completely off-putting. Either show me mechanics that will make it true in play (how does the PHB tell me that dwarves are hardy? because they get Second Wind as a minor action!), or say nothing at all. But long descriptions that are divorced from the play experience, and sometimes are misleading as to they way some power or ability will actually play out at the table, are not very interesting to me. When I look through my Essentials books, I skip over all that stuff so I can see what the mechanics are, and hence really see what sort of fiction is going to be created by using this stuff in a game.
Personally, I found E-fluff mostly just redundant filler, a large-type re-iteration of the italic fluff in each power description. But, yes one stereotypical failing of RPGs is to give a great fluff-text description of something, or put in a cool illo of the same thing, and then have the mechanics completely fail to live up to it.
I don't think you can count on getting fluff and crunch into perfect alignment (for one thing, because necessarily natural-language fluff can always be interpreted in a variety of ways), so instead, you can explicitly let one or the other 'win' and put more emphasis on getting that aspect right. 4e put mechanics first in it's design priorities, so it had clear, balanced, playable mechanics that made it plain what each game element accomplished in play. It left the 'fluff' sketchy, weak, and not always matching up that well, but invited the user to substitute something from his own imagination, instead. There have been games - Storyteller, again, is an example I'm familiar with - that go ahead and put the fluff first and just broadly paint the mechanics, figuring you'll go with what you want, and the mechanics are just a temporary crutch that should work badly, so you'll have an incentive to learn to do without them ("bad rules make good games").
5e, since this is a 5e thread, really, does try to take a more middle-of-the-road approach. The DM is free to change the mechanics as he likes, but they're not officially subordinated to fluff, and re-skinning of fluff, even by players, still seems acceptable - if there's a flavor/mechanic disconnect the DM has the final say in resolving it. That may not be avoiding the problem entirely, but it at least gives permission for the DM to fix it as he thinks will best suit his group.
I find this a chicken-or-egg dilemma then.
Is the dwarf hardy because it has second wind, or does it have second wind because its hardy? Which comes first, the mechanics or the fluff?
In that specific instance, there's no dilemma: the hardy Dwarf archetype precedes D&D, let alone 4e D&D.
D&D has traditionally written from a place of fluff first, mechanics support it. Your proposing that the mechanics come first, and then you can hang whatever fluff you want on it. That is a very radically different way of doing things.
I think it would be more accurate to say that D&D had traditionally mixed fluff and natural-language rules with mechanical jargon. A lot of the unfortunate complexity (complication), steep learning curve - and constant 'rules lawyer'ing of the early games came from that tendency.
But, yes separating fluff and mechanics and letting the fluff be modified to suit by the player was a striking innovation, for D&D (it had been done much more extensively in Champions! 27 years earlier, so was hardly new to the broader hobby). That approach (whatever game is using it) still doesn't necessarily put one 'first' in the character-creation process though. A player can pick mechanics based on preference or optimization, and then adjust or assign fluff in order to justify the results - or, he could choose the 'fluff' concept he's going for, and make choices that mechanically support the concept, modifying their fluff to match the concept if it doesn't already. It does put crunch first in resolution, though as always, the GM is inevitably free to rule or over-rule as he likes.