I the context of d&d dungeon crawls, i definitely prefer very 'pawn stance' style play, with just a tease of character(i'm actually playing a GURPS game like that right now). I think, as others have said, the system and its benefits are a lot more suited to making strong archetypes to do very specific kinds of things in a fantasy world than handling anything. I'd never use d&d to run a game where the characters were anything other than rough-and-tumble mercenaries of various archetypes who really like to spelunk for treasure.
If I want to play a game where the character of the characters matter a lot more, i'd want something with a more robust allowance for what you can make. A military officer with soldiers at his command, a priest who has knowledge and social skills rather than casting divine spells, a scholar, etc. There's a lot of systems that do that, but d&d isn't really about that, it's made a sacrifice(and i think is better tuned to that past 3rd ed) to make character creation easy, and you don't need a guide if you want to be like this strong fantasy archetype, but the sacrifice is other kinds of characters without a lot of shoehorning.
There are significant advantages to d&d pawn stance or very light characterization games- they can handle more players a lot more easily, it's also much easier to handle absenteeism when characters are largely interchangable in terms of the game. You can kill characters more comfortably without much bad blood, nobody's too invested in things, you don't really have to worry so much about giving people chances as a DM. If I had a game where the cleric and her faith were a super important part of the plot and her player missed a session, either that player is going to be unsatisfied that their cleric's spotlight time was missed or the DM is going to have to cancel due to one absence.
On the other hand, if i'm playing a more intricate game, i really do want to know what esoteric things your character knows about, what they can speak intelligently about, and i'd like that on a sheet. In a sense, the D&D skill system seems vestigial, it's a weird list that seems oddly narrow but I do accept that it's replacing a lot of funky subsystems that would otherwise have to be there a la percentile stuff in 2e. Burning Wheel, for example, has a robust skill list, as does GURPS and many other games, and the skill system is central and core, your characters are, functionally very much defined by them, though not entirely so.(I find it awkward that when i was playing BW, their starter adventure, The Sword was trying to mix BW's mechanics with a d&d type situation and I think it's just not suited. I don't think cave spelunking leads to interesting Beliefs or really uses that game's systems well.)