The difference is that your character can frequently act as if their intellect is very different from their intelligence score, but can never act as if their strength is different from their strength score. If the character is too weak to move a boulder, it doesn't help that the player is a bodybuilder. If the character should be too dumb to solve complex, logical puzzles or mysteries, or make good tactical decisions, he can still solve the puzzles constantly and make perfect tactical decisions if the player is smart enough.
It really depends on how you look at it.
The vast majority of the time, players control their characters however they want. No one bats an eye if the character does something or acts in a way that doesn't make a lot of sense related to their physical stats either ...
unless a check is required (such as moving a boulder).
In much the same way, a player can act differently than their intelligence score,
unless a check is required (such as remembering an obscure fact).
Or, for that matter, in terms of the
skills that are based on those abilities. Or saving throws. Or class abilities. And so on.
So yes, abilities don't matter, unless they do. If you make every roleplaying decision, from solving puzzles to choosing how to attack monsters, an issue for the dice to decide, at a certain point you are no longer roleplaying and you are no longer allowing players to make their own decisions.
To a certain extent, allowing players to choose their tactics and solve puzzles and talk to NPCs is not just a part of the history of the game, it's also something that most players enjoy and consider fun.