I think the problem is that different games tend to make different abilities more powerful. A standard textbook D&D game and STR, Con and Dex are the kings of the table, as combat determines everything.Like vancian casting, the six abilities are a recognizable tradition that works less well.
It is possible to clarify and balance the abilities by adding Athletics and Perception to make eight abilities, or consolidating the eight to four abilities.
• Strength-Constitution
• Dexterity-Athletics
• Intelligence-Perception
• Charisma-Wisdom
Both the eightsome and the foursome work well. It is obvious which ability to use, and which not to use. And each gets used about equally often during gameplay for about equally important things. Making Athletics the go-to ability for swashbuckling campaigns enhances the cinematic excitement. Perception merits its promotion.
But is it possible to make the 'classic' sixsome work well?
I cant yet make the six abilities work well, in terms of avoiding ambiguity (like facilitating agility themes, disambiguating Perception-Investigation, Survival-Nature, and so on) and maintaining balance (like Intelligence being equally valuable as Dexterity).
But there might be a way forward. In 5e, Constitution has evolved into a strictly passive ability. It is responsible for hit points and 'fortitude' saves. It seems possible to update Wisdom into a strictly passive ability, relating mental health in some sense. However I am unsure what its mechanics should be exactly, and how to balance it with the rest of the six abilities.
Hypothetically, the structure for a balanced ability system, might look something like the following:
Power Precision Endurance (Passive) Physical Abilities STRENGTH DEXTERITY CONSTITUTION Mental Abilities CHARISMA INTELLIGENCE WISDOM
A knowledge and skillbased game and int and wisdom rule.
A game where interaction with the rulers and power players of the game world happens a lot and CHR can be like having unlimited wishes for a mage.
No matter how hard you try to balance things, something is always more powerful in the context of the game and what is the most likely thing to influence events in the game. I've played in games where CHR was the most powerful stat, Game's where skills were the most powerful things and games where perception was the most powerful thing, along with the games where everything was about how fast you could kill things and whether or not you could survive till they all died. What the DM focuses on will determine what is the king stat.