D&D isn't like Warhammer. Warhammer is just a ton of lore and culture and who cares how it plays. D&D is a mix where it's less about the lore and culture and more about a mechanical system of game design determining how it should be played; one that is dating rapidly and, imo, has presented major friction to adapting to more modern mediums and forms.
I would argue that D&D had mechanical issues even from the start, even in table top roleplaying and in early CRPGs. In particular, some flaws of early D&D (1e and 2e, which are fairly similar, here):
* XP tables are a bit strange. Your XP requirements grow exponentially at first, but then they stop increasing. This leads to leveling slowing down greatly at first, and then accelerating as the requirements stop increasing, but monsters give more XP. (Not to mention XP from treasure in 1e, which led to players being given ludicrous amounts of treasure just so they would level up at a decent rate.) In fact, I am not sure if XP is the right mechanic for table top role playing; it adds a fair amount of math, with numbers the average person can't really handle in their head.
* Healing is annoyingly weak. Basically, for quite a while, your only healing spell is weak, and sometimes you will use it and it will only restore 1 hit point. This means that the spells don't add strategic variety to combat, and would not be worth using at all if it weren't for another annoying factor; resting doesn't significantly heal you, forcing you into a cycle of cast all healing spells (and roll for each spell cast), rest, and repeat until back to full health. One of the best simplifications done in early JRPGs (Dragon Quest and Final Fantasy) was to make inns fully heal you.
* Exception to that last point: Once your priest reaches level 11, she will gain access to the Heal spell, which unlike previous healing spells, is extremely powerful. This creates a bit of a healing power discontinuity, which has been seen in a few other early CRPGs (Wizardry 1-5 and Final Fantasy 1 come to mind, as do the Bard's Tale games (which are even worse because the powerful healing spell is learned by a different class entirely).
* There were some arbitrary restrictions that (unfairly IMO) penalize certain types of characters. First, there's racial level limits; non-human non-thieves can only advance to a certain level; in campaigns higher than that level, such characters are completely non-viable. (Note that the Infinity Engine games do not implement this rule, with good reason, but earlier AD&D CRPGs do; see Pools of Darkness for an extreme example of the consequences of this rule.) Then there's the sexist 1e rule that limits the strength stat of female characters and gives them nothing in return.
* There's also the way that spell slots are segregated by level, which makes no sense (see my topic in the Baldur's Gate subforum), and leads to high level spellcasters having too many spell slots to worry about at high levels, much of which can only be filled with spells that are too weak to be of much use. (Note that this is a separate issue from Vancian magic, in which you have to choose which spells to spend your spell slots on in advance rather than being able to cast any spell that you still have an unspent slot for.)
There are, of course, many issues not mentioned here.