@pemerton @Helpful NPC Thom
These things are colour/not-required in the same way than music having sound is just colour. You could just read the notes and lyrics.
But you'd basically be missing the whole bloody point of the thing.
I'm reminded of a story I've read about Wagner - for one of his birthdays, Cosima arranged for a small orchestra to come to their house to play the Siegfried Idyll. I haven't looked up the book, but in my memory at least this was the first time Wagner had heard it played.
I think it can be easy to forget what that would be like, in a world with ready access to mechanical or electronic recordings.
I don't think that changes the question about RPGing, though: is the characterisation mere colour, or not? For instance, in 5e D&D whether or not a barbarian can enter a rage doesn't depend on whether or not the player is able to portray the character as angry, nor on whether or not it makes sense in the fiction that the barbarian should enter a rage here and now. That's mere colour.
Whereas the portrayal of a NPC as friendly, or angry, affects their starting attituded and hence the DC for subsequent CHA checks to influence them. That's not mere colour: it matters to resolution.
My own view is that the more that a RPG makes the fiction important beyond being mere colour, the more satisfying it is (everything else being held more-or-less equal). There are many different ways of doing this, of course. The example of NPC attitudes is one.
Another is illustrated by one of my favourite 4e powers, Valiant Strike: the paladin gets a bonus to hit based on the number of adjacent foes, meaning that being valiant isn't mere assertion or epiphenomenal portrayal or the sort of "technically wrong" decision that was mentioned upthread. Rather, the player's incentive aligns with the character's valiant spirit, to hurl the character into the midst of the fray.
I also love the 4e Deathlock Wight. It's not just that its visage is horrific: when it turns its gaze on you, you recoil in horror! (A push attack vs Will that also inflicts psychic damage.)
There's lot of other possibilities too, both in combat and non-combat resolution.
Flipping it around: I like Marvel Heroic RP/Cortex+ Heroic a system, and have played it a fair bit. But one frustration with it is that fiction often
doesn't matter to resolution - ie remains mere colour - unless it is "mechanised" as a Distinction or Trait of some sort. So a character can't just, for instance, get a benefit to sneaking or sniping by lurking in the shadows: they have to succeed at an action to create a Lurking in the Shadows asset. This aspect of the mechanics works very smoothly in the process of play, but it can mean that the "scenery" sometimes feels a bit flat. As a GM there are steps I take to try and remedy this, following the implicit advice of some examples in the various scenarios and supplements; but there's a clear contrast with (say) Prince Valiant or Burning Wheel or AD&D or Rolemaster, where the fictional positioning just factors into resolution without needing to be "mechanised".
I believe that Fate may have a similar issue, though I don't have the play experience to be sure.