They have a unique and interesting style of storytelling that actually isn't so hard to understand nor to follow. It's also not non-existent. It's just, as you paraphrased, that the moment to moment gameplay works against that. You're more busy with surviving, battling normal foes and bosses the hundredth time, spending hours just to get an item that explains three more sentences about the lore and story and what the actual fuck happened in this world.
Not having everything spelled out for the player and let them explore the story in the same way they explore the world is quite extraordinary and rare in a medium that – still having issues with telling complex and mature stories with sensible themes – constantly questions the player's intelligence and champions their inadequateness.
I'd love to see that kind of storytelling in more accessible games than those FromSoftware make.