@
Xeviat, here are some other questions you could also ask:
...Do genre conventions support two characters being equally strong, but one being better at Bending Bars/Lifting Gates/Bashing Doors/etc.? Or, two characters being equally "healthy" but one being better at Long Distance Running/Rowing/Hard Labor?
...What exactly do the ability scores represent? Is Strength really the ultimate measure of muscular force -OR- does Strength merely indicate how
effective you are at applying muscular force to attacks, saves, and ability checks? The distinction is subtle and usually doesn't matter, but consider something like racial traits which double your carrying capacity, or consider how the barbarian's rage lets you hit harder and get advantage on Strength checks without actually making your Strength score go up (which is what Rage did in 3E, where it was much clearer that ability scores represented ultimate reality rather than game mechanical constructs). Or, another example might be the Tough feat: if Constitution represents raw health, how does Tough increase your hit points?
...What exactly do skills represent? Are they purely based on training, or do they more broadly cover aptitude from a variety of sources? I just re-read the Skills section in the PHB (Chapter 7) and it doesn't mention training; it instead treats skills merely as
aspects of an ability score, in which a character might be proficient.
...Is there
ever a need for a raw ability check? The PHB (Chapter 7) gives numerous examples, but most either a) involve tools with which you might be proficient, b) could plausibly be folded into an existing skill (the Dexterity and Wisdom examples fit this well), or c) could be folded into a new skill. I'd call out Might for the Strength examples, Endurance for the Constitution examples, and something like "Streetwise/Gather Information/Connections/Social Groups" for the Charisma examples (I'm not sure what to call that skill exactly, but it involves navigating, influencing, and understanding entire broad groups of people). That skill could also plausibly cover the "appraise" example under Intelligence, although tool proficiency might fit better.
I like where you're going with this exercise, as I feel like the skill list in 5E is one of the weaker parts of the system. They tried to give ability scores primacy over skills but it didn't quite work.
