By creating such a game system, all you will do for that type of player is that instead of having a plan for class options, they would have a plan for which adventures they plan to go on and in which order they plan on doing them.
Exactly! And I personally see no problem with players getting interested in what adventures to go on, even if what interests them is what'll happen to their characters and not what the story is about.
This system of "you level up what you use, and your adventures give you your class abilities" would also mean that in lesser danger situations, the party will encourage PCs weak in a certain area to try something instead of the specialist ("you try to pick that lock, Father Priestly. I'll give you some pointers") which might sound a bit mechanic in nature... but it's actually what happens in real life.
(As an aside, I volunteer for marine Search and Rescue. I'm learning navigation, but I'm still pretty green at it. So, when we're on a real call, I'm not on Nav. But if we don't need to be anywhere, or if we're in no hurry to get there, the experienced guys step back and let me try and screw up so I can "level up" my skill in that area. So, my mechanics would actually kind of mirror how people get better at things).
And personally, I think the idea of getting new abilities and skills from the adventures you're on would be cool, because after a half dozen adventures, you'd be able to look at your character sheet and remember adventures you've been on... not just treasure that you own.
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In regards to your comments on "builds" in 2e, that only happened in the Skills and Powers era. In most of the game, there were few chances to "build", and when there were, it only applied to dual-class characters, and weren't at all similar to what we've seen in the post 2e era. Having played extensively from 2e onwards, I can assure you that builds just weren't as big a thing as they are now.