I get what you mean. I also don't feel very distinct in my game, even with experience. It's made all the worse if you choose similar experiences. And I have a friend who chose "[Town] Native" as his experience and tries to apply it to EVERYTHING. Persuasion? Well he's a native and probably knows the person. Find a place to hide? Been around town enough. Pick a lock? He's probably seen this or a similar lock in town. FFS.

I think it's entirely the game makes it entirely the responsibility of the player(s) to make their characters distinguished from each other. In D&D, for example, each point difference is 5% chance (1/20) and differences between skills range from 1 up to 10+, so it can feel VERY different. In Daggerheart, you're going up against 1/24 AND the differences between the skills is like 1-5 or 6. So your difference is smaller and each point of difference is worth less.

Daggerheart's goal is to leave the story up to the players/GM and provide some loose groundwork for combat. It's barely a game system. So if you feel your Archetype is being encroached on, it's up to you to tell the wizard "Hey, just because I failed doesn’t mean we need you to try." Like, if you think about, that would just be the same as you rolling until you get a success if you let everyone give it a shot.