Oh sure. Not something I'd do, and thus the point of this rather lengthy discussion. As a player, I'd be decidedly unhappy if my results were being filtered through what the DM perceives as relevant to the check based on the character making the check, simply because what's on the character sheet and even in the background, is such a tiny slice of what that person actually is. Sure, Bob may be better educated than my character, but, it's not difficult to come up with narratives where I might know some fact that he does not. That he would automatically gain a better result, despite having the same actually die result (modified by all the goodies of course) simply because of the character sheet is too narrow for my tastes.
AFAIC, a 16 is a 16 (or whatever number you care to choose) regardless of how I arrived at that 16.
While, I can't disagree that this is probably the best way to approach things most of the time, I think sometimes, it is appropriate for the DM to take into consideration things that are "on the character sheet" and "in the background." And I can't imagine that, at some point, you wouldn't break down and agree.
Let me pose another example. Suppose the PCs are trying to jump high and pressing a small button on the ceiling of a room that is 15 feet high. You call for an Athletics check to simulate the combined difficulty of jumping high and touching the small button in mid-jump (from the Player's Handbook: "In some circumstances, your DM might allow you to make a Strength (Athletics) check to jump higher than you normally can.")
Would you really say that the DC (or alternatively the bonus) is the same for all of the following PCs:
* A 3 foot tall halfling.
* A 12 foot tall ogre.
* A bullywug (Note that the bullywug has the special ability: "Standing Leap. The bullywug's long jump is up to 20 feet and its high jump is up to 10 feet, with or without a running start").
* A PC wearing boots of striding and springing (Note that the description of the boots says: "you can jump three times the normal distance, though you can't jump
farther than your remaining movement would allow").
* A PC who is using a 10 foot pole (written as equipment on his character sheet) to try to press the button with a relatively short jump.
* A PC using the gust cantrip to give himself an extra boost at the same time he makes his Athletics check (this actually happened in the last adventure I ran)
* A PC using a levitate spell to lift himself 8 feet in the air (but no more than 8 feet because he doesn't want to make it too easy)
* A PC whose character background includes the statement: "As a young child, Jack's legs were severely mangled in a crocodile attack. Although he is quite strong, all his strength is in his upper body and his legs are very weak."
* A PC whose background includes the following statement: "Mary is a champion basket ball player, particularly well-known for being able to jump high and dunk the ball."