Ok, so what if you envision your character as a consummate diplomat, secretive yet suave... and all you have on your character sheet are stats like "stabbing people" and "being really strong, in order to stab people better" ? Would you say that such a character sheet "does not support the vision" of the player ?

Obviously I would say exactly that.

Said by me:

game-mechanical challenges — whether these be combat, social interaction, assorted noncombat challenges ("we need to cross this chasm"; "we need to infiltrate this castle"; "we need to figure out whodunit"), or anything else that is handled by game mechanics in any way

Also said by me:

[Game-mechanical challenges] is not necessarily combat. It could also involve various non-combat skills, among other things.

So, I'm not really sure what you're objecting to. Are you under the impression that I was advocating just being good at combat, and being bad at everything else? Regardless, even, of how much of the game consists of combat? I'm not sure what I said that gave you that impression.

Some minor notes, don't take these as anything but tangents:

Note that the player's diplomatic skills would be absolutely useless in combat

You'd be surprised... there are some builds out there that do crazy things with "non-combat" skills.

depending on the plot, it may be highly unlikely that diplomacy will play any significant role during the course of the game. In fact, in D&D specifically, combat is overwhelmingly more likely to occur than negotiations.

Depends on the players and the DM. For example, just recently, in my aforementioned campaign, I was all set to run a combat encounter, but one of the PCs instead negotiated his way out of it. It happens.