There is something I only recall seeing in AD&D 2nd Edition (revised) and not repeated since*: high stats that are giving sort of mini-powers, such as high enough Intelligence allowing the see through 1st- and 2nd levels illusions automatically or high enough Constitution giving an actual regeneration. Even without mini-powers in a strict sense, this edition handled high stats as special cases even for more mundane derivatives, such as ability to 100% survive system shock or learn all spells per level instead of progressively bigger chance/amount of them. This kind of treatment gave stats something more than just being a number, a sort of threshold after which stats switched from just quantity to a new quality.
(*) within my limited amount of system known
High stats in 2nd Ed gave those mini-powers because they were supposed to be rarity; in this sense 2nd Ed inherited non-linear stat adjustments from earlier editions. Today starting with 20 in one stat in PF, 4th and
5th is nothing unusual, and is more often a given than not. In 2nd ed, however, there were very few ways to increase stats through few magical items (which you couldn't buy or craft), and no spells or class abilities, AFAIR, allowed for such boost. Numerically, mini-abilities sat exactly on tantalizing line of 'maybe-possible even during the character generation if one is lucky' and 'I just need one more point to get it' – within the reach but not easy to obtain.
Second Edition in general has a curious place in my perception: much heavier and much more cumbersome than OSR-preferred, lighter systems of earlier editions but also not as powers-abundant and (for the lack of the better world) comfortable/convenient as 3rd, 4th and 5th. If it was anything, it was a chaos: a overflowing, convoluted, shaky mess, with what felt as arbitrary limits, arbitrary elements, arbitrary connections within its arbitrary limits and elements and exceptions on top of exceptions. Out of all editions, to me 2nd Ed is the one that is like a soil – dark, crumbling and full of strange worms. Maybe stats as mini-powers didn't work and this was why they weren't repeated later. Maybe in both aims for the balance (which became a prominent for the 3rd, 4th and 5th Editions) and for lighter, less-powerful-characters systems (which is common in OSR) this idea was too much of a mess.
But I am wondering, what if to try to combine this idea with more streamlined stats of nowadays. What if until certain number – say, 18 or 20 or even 30 if you aim for PF-like numbers, – stats give linear beneficial modifiers and after that the stats no longer give a better bonus, but instead a few gradations of mini-abilities useful for pretty much anybody.
Superior strength would give an ability to dual-wield increasingly heavier weapons
Superior reflexes would give some bullet time
Superior fortitude would give regenerating health
Superior insight would allow to bypass some illusions automatically and/or give some occult awareness.
Superior willpower would allow to bypass or offer advantage against some charms/fear/compulsion effects automatically
Superior charisma will allow to weaponize one-liners.
[these examples are partially taken from AD&D 2nd Edition and partially from videogames (thanks to Realms Of Gibbitude for the idea)]
The main idea here that mastery through the class or spells can allow for the same things and maybe even faster (such as when fighter can learn to wield two weapons easier than their natural strength would allow them to do) but these mini-abilities can still be useful for those who want to play non-standard archetypes of two-weapons wielding mages or occult investigating fighters and by change or effort got these stats high enough.