MMmm... so...
For 6e? I dearly wish they'd step -back- a few editions.
5e having strength determine your jumping distance is pretty nice... but what about Intelligence, Wisdom, and Charisma?
Keep the ability scores and have the different quantities apply different exploration and social traits -alongside- skill-use.
Strength determines your jumping distance. Intelligence divided by 3 is your automatic languages at level 1, before class or background grants more, Wisdom gives you a sight-range for perception checks by determining how easily distracted you are, overall.
Not sure what to do with Charisma and Dexterity, but Constitution already determines how long you hold your breath, just make it 1 round per point of Constitution.
Heck... make stuff like this -baseline- to every skill, where your attribute score determines some aspect of the exploration or social pillar, and then your skill proficiency and bonus determine the result.
How about Persuasion can be done on a number of people equal to your charisma score divided by 2 at a given time, early on, and later on it's score x2 or x3. Allowing you to start out persuading a handful of guards or many a small crowd of legbreakers, but once you've got a few levels under your belt you can persuade a mob the side of a city block to stop a lynching, like Emperor Norton the 1st, Ruler of the United States.
Meanwhile you can Perform for a crowd equal to your Charisma Score at level 1, and that number grows as you gain levels at a similar rate...
And you can only Deceive a fraction of as many people at the start of leveling.
That'd certainly make things interesting.