This is what I'm saying is not true in most of my RPGing. When characters fight; or when a character tries to pick a lock; there is something happening in the fiction. The roll of the dice doesn't represent that something. But it contributes to how we - the game participants - decide what is happening in the fiction.
IME, Most players conflate the reason for the roll with the roll itself; they don't see them as separate in the way you're arguing for.
When the die itself is tied to the action or the weapon, your insistence of separation falls even further from the phronema of most players.
For example, in MHRP, one can in fact choose to color code one's dice so each die can be tracked for what it was generated by for narration of the outcome.
EG: I put in a red d8 for my solo score, a blue d8 for my "Shameless Glory Hound" distinction, a blue d10 for my Magic Sword, a red d6 for my shield, and a green d8 for my Melee specialty. Rolls (roll/sides) :
4/8 2/8 2/8 5/10 4/6 ... so my best dice are the Magic Sword at 5, and either the shield at 4 or the solo at 4... with the blue or the green d8 as my effect die.. so Swinging wildly, with the sword and shield, I show off immensely as I attack (with a 9 result and d8 effect). Each die in that case can be representative of specific elements in the fiction, and the choice of which to keep can be used to determine the narrative qualities of the success or failure.
Likewise, many simpler dice pools the dice can be said to represent some factor in building the pool; in VTM, for example, my roll to intimidate the puny guy might be Strength plus Intimidation, and if I can demonstrate it with a strength feat, possibly adding my Potence to the pool... and rolling them each on different colors can allow a nuanced read of the result... say, Str 4 in red, Intimidation 3 in Blue, and Potence 2 in green... and target Willpower 5:
9 7 3 10 9 8 1 9 8. We'll cancel that blue 8 for the blue 1.So 3s from strength, 1 net from skill, and 2 from potence... Note no open end on the 10 because no specialty used. breaking the chair with one arm and stepping into the personal space of the victim, "You will be just as easily broken if you don't coöperate," I say, as I flex...
While :
5 1 3 3 1 1 3 1 2. a botch... -3 successes... Attempting to break the chair, I lose my grip and send it clattering, the result clearly showing I'm off my game, and inspiring no fear at all... at least he knows I can one hand throw the chair...
Theoretically, an additional die for a suitable weapon might be added as well, and a fourth color to represent it.
Note that the idea of tracking which dice came from which source isn't my own; I got it from a forum post for VTM 1.0 very long ago. Don't recall if USENET or WWIVnet... or CIS...
The dice in those pools are there to represent those factors from the mechanics and having presence in the fiction. The distinction that the die itself isn't a representation of skill, it's purpose for being rolled is, and the purpose gives meaning to the dice.
(All rolls made using the FFG/Edge Genesys die roller for iPad on a Mac. Yes, it has normal dice.)