I don't disagree with you about the mechanics, and some of their emergent consequences. But I think I do disagree a bit about how much this produces story.It was not the goal but oD&D even had significant mechanics that strongly encouraged the growth of stories and were dropped from later editions although would fit very well in modern narrativist games:
It's not what he intended but genuine old school games, like many modern post-Forge games IME have more emergent and organic storytelling than most trad games.
- XP for GP made the PCs strongly motivated to do stuff and towards not always doing the obvious
- Hirelings and the soft cap changed the relationship of the PCs to the world, from one of a large mob to one of a small party, to semi-retirement as movers and shakers; that's a story
- Asymmetric class balance that balances over the career not the adventuring day generates its own stories in a way modern D&D doesn't
- Power being based on loot is almost Roguelite and makes the practical characters far more unique and thus the game more replay able than builds, and this leads to interesting stories
The main RPG I've played (GMed) recently is Torchbearer 2e. It certainly ticks your first box (gp aren't XP, but there are other features of the game that makes every player motivated to have their PC obtain loot). But exactly this feature tends to somewhat lessen its story-esque orientation compared to its sibling Burning Wheel.
Like classic D&D, TB2e also has a strong inventory management aspect. And while this is interesting and quite fun in play - eg it's the only RPG I've ever played where so much turns on whether or not the PCs have shoes, and where wearing out your shoes hiking is a serious risk - I don't think this necessarily conduces to story.
I've not done any OSR RPGing in the strictest sense. Over the past decade, the only classic sort of play I've done is actually classic - sessions of AD&D (using my own version of the rules, that integrates a few bits of OA, UA and 2nd ed PC build) and Moldvay Basic. But I did recently run a session of Mythic Bastionland, and anticipate playing it some more. And in play, I was very struck by how gamist it is - much more than I anticipated, meaning that the relationship between play and the obvious thematic elements of the game was quite different from what I'd expected.

