Is there a reason you responded to my comment but ignored my question?
Once again, it has nothing to do with the "rules". This is not changing a rule, any more than is having a Sorcerer narrate his spellcasting as throwing playing cards.
Probably not all that much different, that is not how spellcasting "works" in D&D. Would you simply be ignoring the V,S,M components or would you consider "If you can't provide one or more of a spell's components, you are unable to cast the spell." to be "not a rule" by some definition?
It only changes a rule if you let the narration drive the mechanics. If the Sorcerer suddenly decides that he can throw a few extra cards, or even if the DM says "Sorry, you're facing into a hurricane force wind so you can't throw cards", then the narrative has crossed the line into mechanics.
It has already crossed the line into "mechanics" though, you may deem them "fluff" by some definition but the rules describe how spells are cast in D&D, going outside those rules is going outside those rules (not a bad thing).
Funny that you mention how this reminds you of 'younger players' wanting to be good in every way. It seems like one of the oppositions to this sort of RP is based on the fear that some players will try to cross that narration/mechanics line, once you let them control the narrative. And they might. And maybe that's a good reason to not allow it at your table. But that's very different from saying that it breaks a rule.
I was hesitant to mention this because it might be taken the wrong way, but it didn't feel right to ignore my experience because it might bother someone. I have no problems dealing with players who "might cross the line" my players are awesome.
I do prefer using definitions that are consistent and I prefer following the rules if it makes more "sense" and is less likely to need all sorts of juggling/retcon/things just not happening lest they "spoil the narrative" even if they make sense
ie; Big burly Hobgoblin with "low strength" getting charmed into using his supposed muscle mass, or deciding to use it, or watching someone they care about die because they aren't going to use it, etc.
If there is a big enough reason to go against those definitions, I have no problem with it, and in that case I have no problem admitting they are not BTB. I like lots of things that aren't BTB.
The passages you quote from PHB are not rules because they don't define any mechanics. HOW do they measure natural athleticism, mental acuity, etc. There's no function, no equation, no rule. Some text is simply meant to add color to the mechanics.
Within D&D, you are intended to measure them with the ability score, simple as that. They are an abstraction intended to describe the things that the book says they describe.
"... But are you seriously going to tell me that a player who describes himself as helmetless and without a coat of arms (backstory: too poor for such finery) is breaking the rules?
Nope, I would not say that they were "breaking" the rules, they are simply not playing the subclass BTB, which is great if that's what's desired.
I would ask you to look at it this way (and it would be really awesome of you if you did);
When you read a document and it is prefaced by a definition of terms as are many technical, legal, or other documents, do you normally think "These are the definitions that are intended to be used for these words within this document?" or do you think "They probably intended me to swap out these definitions for ones that in the real world mean the exact opposite thing."