RE: Gamist Roots
There's this myth out there that D&D has "gamist roots". The narrative goes something like this:
Chainmail came first; it was a wargame. Then came 1e, which was a role-playing game that listed movement rates and spell areas in inches. Then came 2e, full of narrative pretensions and White Wolf envy. 3e put things back in the dungeon, and 3.5 put minis back on the tabletop -- but these rules were also simulationist, because the monsters had ability scores (gasp!). Now we have 4e, which foregrounds the game qua game and might as well be a minis skirmish game, but that's okay, because it all started with Chainmail.
But that's a bloody caricature, libelous in its lack of nuance. Even in the days of 0e and 1e, the story-telling, world-building, and play-acting components of the nascent RPG hobby were just as prominent as minis battles and so-called "funhouse" dungeons (which, for some reason, are looked back on as "gamist" because if the supposed illogic of "rooms full of monsters, traps, and treasure") -- if not moreso, since role-playing elements were the new thing, the very features which set D&D apart from wargames.
4e has not returned to some mythical point in the past history of the hobby when miniatures and "roll-playing" were all, and "role-playing" had yet to be invented. The role-playing was there early on. 4e is, simply put, the most unabashedly gamist incarnation of D&D ever. But that, in itself, is *not* where the dislike comes from. There's nothing *wrong* with 4e taken on its own. The probelm, as so many have already noted, is legacy. 4e is a good game, even a good RPG, but it's only passing-fair D&D.
When you line up all the sacred cows, fluffy and crunchy alike, and slaughter them wholesale, you're going to have unhappy customers who preferred live cows to hamburger. Some of us can't imagine a D&D that doesn't have hit dice, or wandering monsters, or the mage reaching 5th level and learning his first 3rd level spell. Never mind the fact that tiefling warlocks, shardmind ardents, and dragonborn warlords do not resonate archetypically with longtime players of D&D. 3e kept continuity with previous versions of the game: it had hit dice and spell levels and random encounter tables. 4e does not have these things: it has broken with the past in a very radical way -- too radical for those who profess an avowed dislike for it.