If you're using a system where stats explicitly aren't present or aren't representative of aspects of your character, or your don't have any extraordinary stats to roleplay, then of course your situation would be very different. But if the stats are there, and they're indicated as modeling something about you, then IMO that should be represented in how that character is played.
Honest question, you mentioned that they're there to model some aspect of the character, how do the other things that form the model of those aspects factor in for you?
In modern D&D terms, I'm referring not just to the Intelligence score but also the Intelligence modifier, the Proficiency Bonus, Expertise, and the d20.
In terms of determining this aspect of the character, their intelligence, do you see it as being modeled upon all of these mechanics in aggregate?
I ask because I'm just wondering if the use of Intelligence score as the example is being used explicitly just the score itself or as shorthand for this aggregate. In my eyes, of those various mechanics, the score itself seems the least involved. Each of the other mechanics have a greater impact on this aspect that they collectively model.
I had a character whose Int-based skills ranged from +14 to +24 by the end. If I drop the Int score from 18 to 8, the build is still viable, and it would have reduced that to range of +9 to +19. An Int 8 with a 50% chance to beat DC 30, that can never fail at DC 20, in Arcana.
I don't necessarily mean to say one shouldn't roleplay that Int 8 as a bit dumb. They may be really good at Arcana but a base Intelligence check, no proficiency or other bonuses, and they're out of their depth. This is more to gauge if the topic about Int 8 is more reductive than intended, that in practice the aggregate has greater effect.