Forgive the rambling. TL;DR: Ability scores should be potential rather than literal description, decouple bonus from score and reduce the score to improve your bonus and gain related benefits as you level up.
This we know for certain: In D&D the mightiest barbarian in the land and a 18-year old strapping young woodcutter can share the same STR score if the dice decree so. But, of course, a zero-level classless character is preponderously weaker than their 10th-level, hidebound counterpart, regardless of what their relative “abilities” are. In original D&D, ability scores barely have any effect at all after character generation and a few starting bonuses, except to determine experience point gain rate. So we have a contradiction: supposedly we can create any character within the bounds of the system (which tells us a STR of 18 is mighty indeed), yet we must simultaneously only create proto-characters, weaklings we can only see grow with time and experience. Ability scores simultaneously describe and lie, the true power of a character lies in those statistics that have no real-world connotations, in level and hit dice and to-hit bonuses and spells known. Hence the existence of so many games that have reduced or done away with the ability scores altogether.
And in games where this disparity is addressed, where the outcome of most actions is decided by, for example, rolling under ability score, the opposite is often true. Characters created are in their final forms, unable to grow or improve unless they come into contact with external sources of power, side gains of equipment, mutations and alterations rather than straight up improvement. This is also somewhat uninspiring, in that it tells you your lot in life is decided by age and page 0, before your character’s journey has even begun, and that only bargaining with cthulhu or looting long dead dwarven forges can improve it at all.
So I propose some theoretical joinder. Let ability scores not be what your characters are, but what they could be. It isn’t that STR 18 means your character is the strongest specimen of human the lands have ever seen, it is that their potential for growth in Strength is considerate, and their potential quite wide. Hence the minor bonuses- unused potential provides only glimmers of improvement beyond the baseline.
For example, in this system STR scores of 7- would provide a bonus of -1, 8-14 of 0, and 15+ of +1. So far, so normal. Ability checks are made by rolling d20 and adding the bonus, aiming to roll above 12. Now, however, when you level up, you have a choice of decreasing a stat by 1d6 (so long as it is greater than 0) in order to increase their bonus by 1. Each stat could also provide benefits when reducing it’s “raw score” - STR gives attack bonuses, DEX thief manoeuvres, CON hit dice, INT skills or languages, and so on. You are, in essence, “cashing out” your character’s potential for growth with experience so that they can realise who they were meant to be, their newfound strength commensurate with the slow ticking of the stat towards that inevitable 0.
Attacks which damage ability scores now no longer hinder your actual performance - they drain away your potential, who you could be, what you might do. Age, too, could do the same. Thus we also have a lifespan as a mechanic. When a character runs out of all ability scores, that is the signal that their natural lifeforce has been expended, and that it is time to make a new character and move on. Powerful magic could extend your raw scores and hence your natural lifespace. Elves might regain 1d6 in any score by performing magic rituals. And, of course, those with precious little potential can still seek out the other pathways to power, the less conventional, the darker and more desperate.
I’d love to hear your thoughts on the matter, if any.