I would say the DM can and should give a character a better chance to hit (or worse), depending on the player's description. It's not about the level of detail or how engaging it is, but rather the goal and approach relative to the situation. The advantage or disadvantage mechanic is great for this purpose. Take a risk to get behind the hobgoblin shield-wall, for example, and I'm inclined to give you advantage on your attack if you succeed. The player has carefully considered the description of the environment and done something in the fiction to try and better his or her character's chances of success. The same goes for trying to bypass or disable a trap. The "how" of doing a thing should be among the DM's considerations when adjudicating the result in my view.
The trouble here is two-fold: First, the purpose of the die rolls is to obviate a requirement for narrative detail. Second, the descriptive method works for some die rolls and not for others, making it inherently unfair. Third, rewarding some players for narrative unfairly penalizes other players.
First, as I recall - and I'm operating on decades of memory here, informed by GGG, countless Sage Advice columns and other sources - the die rolls are
supposed to be a shorthand. "I check for traps" and rolling dice
is supposed to represent detail which the player - not necessarily the character, but the player - probably doesn't know. "I check for traps" and rolling dice is shorthand for stuff the player's rogue knows to do, like "I run my fingers gently along the base of the monkey statue, attempting to determine if the platform has a specific kind of trap." The player is not a skilled thief. How the heck should she know what to do?
In just the same way, "I attack with my bastard sword" and rolling dice represents "As I transition my longsword through
mezza volta from
porta di ferro mezana to
posta frontale ditta corona, I seek an opportunity to bind under the orc's guard and offer a
sottano to his midriff." Here you're rewarding a player for knowing the
Fior di Battaglia of Fiore dei Liberi. Even if she just says, "I feint to the orc's face before dropping the point to his midriff," you're still rewarding the player. How many players do you think know how to use medieval weapons? I mean for real? I know maybe a dozen gamers who are proficient enough in WMA to offer a plausible detailed narrative of a fight.
As a final example, "I cast
fireball" and rolling dice represents "As I mash together the guano and sulfur in my left hand, I form the Sigil of Hendricks with my right, drawing it over and across the third chakram, as my master taught, before flinging the raw magic at my foe." While, unlike the combat sequence, there's nothing which can be called realistic or not in this, it still unfairly rewards the player who is good at inventing plausible explanations of the V,S,M requirements of the spell.
This is to illustrate that you are rewarding the
player for out-of-game mastery of knowledge or creative talent, not the
PC for in-game actions. On the one hand, I like that, because it rewards players who dig further in to that of which their characters are capable, and it adds to the narrative of the table. On the other, I loathe it, because it unfairly penalizes those who don't want to do that, or can't for some reason, or are new to the game.
I think what happens is what the DMG warns against when using an approach where the DM calls for a roll for just about anything a PC does: "A drawback of this approach is that roleplaying can diminish if players feel that their die rolls, rather than their decisions and characterizations, always determine success." (DMG, page 236)
I prefer the "middle path."
Oh, me too. It's a bit of a poser, this. I don't think there's a good answer, other than discussing the possibility of check die-mechanic modification based on player knowledge and narrative addition when expectations are under discussion before character generation. If everyone agrees that it's okay for only a few players to receive in-game benefit from out-of-game creativity and/or knowledge, I think it's fine to do that.
To opine that simple checks are less than worthy, as the OP did, reeks rather strongly of BadWrongFun.