ability scores as potential rather than realised ability. I wanted to expand on that idea by discussing how one might export the functions of AD&D 1e's ability scores to character class and level. (Briefly: the idea here is to keep the game more focused on these latter qualities because of verisimilitude and fairness. It makes sense that skill is decisive and reducing the impact of random factors in character creation has long had an appeal.) I've chosen Strength to start the discussion because it's the first in the book, but also because its AD&D functions are highly diverse.
Arguably, the most important function of AD&D Strength is to modify the character's maximum encumbrance. This is an unfortunate rule, as it cuts against Gygax's statements elsewhere that encumbrance is not strictly weight, but a kind of aggregate rating of "how difficult it is to move this thing". The main reason for tying strength to encumbrance is to restrict heavy armour to very strong characters, but this is more or less baloney. Armour just isn't as difficult to move in as Gygax's sources made it out to be. I would buy into an argument that stronger characters have larger bodies - and therefore more space for strapping things onto themselves - except that AD&D does not penalise demi-humans on this front. (Perhaps it should!) I think that moving this function over to level is low-hanging fruit: it's easy to see how more experienced adventurers would be more adept at packing their kit, even when dealing with novelty items. Given the likely Strength scores in AD&D, setting the base encumbrance maximum for a 1st level character at 600 coins would not be unreasonable, provided that there was a solid armour option that did not chew through more than half of this budget, with a upper boundary for high-level characters of about 900 to 1200 coins.
Next is the matter of Opening Doors. I generally feel that this is a tedious exercise and that what is being determined is not "can the door be opened?" but "how much time and noise will be created in opening it?" It wouldn't be a far cry from the usual effects to boil the thing down to a single six-sider with 1-3 signifying that the door is forced promptly, 4-5 showing that it took an additional round, and 6 indicating that the party spent two rounds working the door with levers. Is there really a need to modify this? Yes, but the exceptional cases can be subsumed into Bend Bars/Lift Gates. This function was essentially a reward to fighting men for their high strength, giving fighters a useful ability for navigating the dungeon. Note the similarity with the thief's exceptional agility - the same logic could apply, with Bend/Lift becoming an ability reserved for the fighter and its subclasses, and the chance of success dependent upon level. The logic here is that a character's potential strength (the ability score) is inferior to the fighting man's realised strength (level). Aside from the usually understood functions of Bend/Lift, the percentile could apply when a fighting man attempts to force a door (giving a chance of "kicking in the door" or otherwise opening it rapidly enough to gain surprise) or a magically-held portal (replacing the parenthetical odds in the PHB).
Finally, there's the matter of adjustments "to hit" and damage. I tend to think that the former is best incorporated into the tables (although this would require new charts), while modifiers to damage wouldn't be hard to smear across the fighter's level progression.