Gumshoe is like that. Your character doesn't have attributes like Strength or Intelligence they just have Investigative and General skills. Maybe your character has a high Firearms skill because he's really dexterous and nimble, or maybe he just spent a lot of time on the range, either way that's up to you to decide. Of course it's not just the story that has demands it's also that we're playing a game and you need rules. In D&D, they set up the rules so that attributes have an impact on saving throws, skills, and maybe some other things I'm not thinking of right now. If you want to get rid of attributes you need a whole different way to determine skills and saving throws.
I recently rediscovered the Freeform Universal ttrpg which doesn't use ability scores. It's all narrative and it's a fun, easy system that uses 1d6 for task resolution: "even" rolls = different degrees of success, while "odd" rolls = different degrees of failure.
It's so much more narrative: in books and film, no one knows how much a character can lift or how many hit points they have or what their I.Q. is. Characters just DO THINGS and the story tells us what the characters can do. There's no numbers getting in the way. FU allows that same freedom. I mean there's the physics of the setting and the group decides what kinds of expectations that creates, but there's no ability scores or saves or any of that archaic math associated with most ttrpgs. A FU group could easily RP a fantasy tale set in any D&D setting because at its heart tabletop roleplaying is a narrative experience. The math came from wargames and isn't necessary to tell great stories.
For me the abilities matter. Skills are details to describe learning from training and experience. But the abilities are the talents, the general kinds of things that a character will tend to be good at even without training.
This is why prefer to call the abilities, "aptitudes".
Aptitudes sketch quickly the character concept in terms of competence and approach.
I agree abilities matter. What I was getting at is the math that defines the abilities doesn't. Ability scores are just mathematical fluff.
One of the reasons I play RPGs is because I like having mathematical constructs and abstractions to help define the characters (and actions, etc.). While the idea of "ability scores" is not the only way to do this, it's a relatively elegant and intuitive way to communicate large amounts of information, both as a story description and a game mechanism.
I'd be fine without ability scores as long as you can figure out another way to empirically model the characters in a way that makes sense in whatever game you're hypothesizing about. For games like D&D, though, it's generally a case of "good enough". Personally, I prefer to only reinvent the wheel when someone can show there's a benefit, but some folks do it for fun.
That sounds a lot like ability scores to me, just ones that have been tailored to the game. I suppose the line between abilities and skills may be blurry at times.
IME abilities in ttrpgs can be defined narratively as opposed to using numbers, and a more narrative system "moves faster" because of it. Or
could move faster - there's unspoken systematic variables here.
They are just some sort of abstraction to help define characters that we can use in gameplay for challenge resolutions. We don't need ability scores, but we need some sort of abstraction. There are other systems out there, for example tags that define your characters and can be applied to resolution checks as boni or mali.
I agree we need abilities, but that IMO words (narration) define abilities and what they do better than numbers. Staying with Freeform Universal vs. D&D: if a player wants their PC to lift something heavy, with D&D the GM's usual response is "What's the character's Strength score?" Then there's the micro-game of mathematics as the GM and player figure out if the PC can "do the thing".
With FU, if a player wants their character to lift something heavy, as long as it doesn't upset the setting expectations of what that kind of character could do, the player just narrates Thangor lifting the 300-pound sack of gold.
Sure, we've rolled for things for decades because D&D and nearly every other ttrpg have these numeric obstacles to negotiate in order to tell the PCs' story. IME that meta-game of "1d20 + Ability score + magic bonus + blahblahblah" not only isn't necessary, but it impairs the experience of playing the role of your character.