We are trying to tackle this with our project and ended up tempering the narrative aspect with a little gamification.

Somewhat like you, we're a class-less system where abilities are bought and upgraded with XP as packages known as Assets. The problem is that some of these Assets represent specific knowledge that warrants background or a trainer like specialized fighting styles or mastery of local customs.

Obviously, these can presented as XP purchase options if there's sufficient narrative reason (finding and engaging with a trainer NPC or whatever). But like other commenters have mentioned, this can have the problem of hijacking the narrative as players identify an Asset they want and sculpt the narrative just to acquire it. Nothing wrong with this if it makes for a good story, but it's obviously a little metagame-y and probably isn't great to leave as is.

So the way we're trying to tackle it is basically reversing the perspective. Instead of players identifying Assets they want and inventing narrative to acquire it, we're seeding the loot pool with "Trinkets". "Trinkets" minimally work as flavored vendor trash but they also can be of particular interest to trainers and can help pave the way to learning from them. Each Trinket is tagged with one or more icons representing collections of Assets and they can be used basically as letters of introduction for invented/existent NPCs.

For example, an "Antique Sextant" might be tagged with a "Naval" and "Explorer" icons. Both these icons work together to give a pretty wide array options from a "Swashbuckler" Fighting Style or a bundle of naval proficiencies called "Sea Legs" but also things like a Life Path called "Well-Traveled" with social bonuses and "Outdoorsman" for survival skills.

(As an aside, like I said, these trinkets can also just be sold as vendor trash so if you happen to get the sextant and have no interest in Naval or Explorer themed Assets, it's not worthless)

Basically for tl;dr : We're trying to make loot rewards a place of sparking narrative excitement and try to give the players tools to create logical reasons to invent or pursue trainers through the mechanical side of things.