But Old School had plenty of mechanics designed to reinforce narrative. Race as class and level limits to make it human centric. Gold for XP to encourage players to be greedy sword and sorcery types. A progression to ruling kingdoms at high level to reflect Conan's story.
They were just largely ignored by the player base...
Class level limit is more about degree of power, and less about kinds of flavor, but I agree its purpose was to enforce a humanocentric setting, where at least a handful of elites of the highest level humans controlled the setting. It is a setting decision, rather than a character concept decision.
I view "gp for xp" as a "videogamey" points score accumulation, and its narrative implications accidental. It has little to say about character concepts, per se, but does encourage the old school D&D mechanics overall to be more "gamey", a combat game. Hence, old school has a psychological schism between combat gameyness
versus narrative immersion, where tables can play one game without the other, or alternate between them as different kinds of games for a same character.
At mid-tier old school did have a "build a fortress" segue into a different kind of game, that was more like Risk (and compares to the Game of Thrones tv series). This may or may not have happened at a particular table, but there were mechanical distinctions between classes, that implied character concepts, such as Wizards building a "tower" for their kind of fortress, and Clerics building a defacto church for theirs. Players often never reached these levels, as the game itself started breaking down due to wild mechanical imbalances, and were minimal anyway with only a sentence or two, while the DM was entirely responsible for how to make the suggestions workable in game.
The old school mechanical enforcements of a character concept were minimal, subject to DM fiat, and even then nonsystematic, ad hoc and entering the design randomly. Any attempt to generalize and balance the mechanical elaboration of character concepts ends up new school, with more sophisticated and diverse mechanical options to specify each narrative character concept.