D&D PCs are defined by two things: ability scores and level/class/skills. The unsolved conundrum of D&D is how to balance these two sides in a simple manner.
In OD&D, abilities played a relatively small part. This is fine, but not extremely popular. In AD&D, the influence of ability scores on spells, features, combat, etc., was remarkably increased. Still, level was more important. A level 10 fighter with low Strength and low Dexterity will beat a level 1 fighter with high stars 100% of the time. Eventually, skills were added to the mix.
B/X (and clones such as OSE) has a simple alternative rule for ability checks: roll 1d20 under your ability score. Extremely easy, but also limiting. It puts an upper limit to ability scores. It forces you to roll low - unlike most other rolls in the game. Eventually, it would force modern games to add ability scores to monsters, adding unnecessary complexity to the game.
The worst part, however, is how this roll remains unchanged from level 1 to level 14. A 14th level fighter has the hit points of 10 starting fighter, but is not stronger, smarter or wiser when it comes to ability checks (despite being able to survive a 100-foot fall and great at saving throws). Worse, even the abilities he has used for 10 or more levels repeatedly (hearing noises, forcing doors, finding traps) do not improve at all.
AD&D 2e and the Rules Cyclopedia, IIRC, try to add a set of skills (LOTS of skills), in which PCs can improve... that work differently than thieves' skills, making the game more confusing and complex. While I love both games, I'd never play them as written again, for this reason.
|I wouldn't dare.|
Well, you might go the opposite route with something like The Black Hack or Knave: ability scores are king, and, while level doesn't affect your ability checks directly, it raises your abilities, thus helping you indirectly. You can even use "roll high" like everything else in the game (or roll low for everything). However, this makes class a lot less important (Knave gets rid of classes entirely) - and classes are one of the most popular aspects of D&D. Classes are also very convenient shortcuts, especially for worldbuilding.
The "Solomonic" solution seems to be similar to what 5e (and modern D&D in general) does: half your bonus come from ability score, half from class. This necessarily makes the game more complex than ignoring either abilities or levels, but seems to be the most popular solution.
It is my preferred method as well. Dark Fantasy Basic does something similar, giving preeminence to classes/skills but allowing ability modifiers up to +5 to influence on almost everything. My upcoming Old School Feats, to be used in conjunction with B/X, OSE, etc., makes heavy use of ability scores and allows PCs to increase their ability scores as they level up.
But there is no ultimate answer to this question. B/X, as written, is one of my favorite games: it is simple, quick, fun. Likewise, games that simplify the rules to make heavy use of ability scores (The Black Hack or Knave) and little else are also extremely fun - I recommend both.
And, for my own games, I'll probably be always in the look for a happy medium: adding classes and skills to Knave, adding ability score improvements (and maybe even general skills) to B/X, OSE, and so on, or creating my own hacks with both methods. Keep trying until a find a porridge that is "just right".
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