1. I'm not at all convinced that the GNS model is valid. In practice, it seems more frequently used to support whatever preferences the person touting it already has.
2. Fate and Dungeon World and similar games already exist. If I wanted to play those games, I'd play them, rather than hack a BRP system. I like BRP because it's not either of those two.
3. You can have a system that allows character or choose when to be extra effective, or pushes motiviations, backstory elements, etc without having Fate-style declarations. See the One Ring, Pendragon, Burning Wheel.
4. In my experience, allowing players to define significant things in the world has the opposite effect of motivating them, investing them, etc. I've played a bunch of those games, and most of the time players end up invested in something the GM made up, because they DIDN'T make it up, and it seems more real therefore.
5. Allowing major Fate-style Declarations sets up a weird interaction. Making a character, playing that character, makes most people invested in that character. They want the character to be succesful (at least from that character's perspective) in a scene. When this happens, you're going to go for whatever Fate-style Declartion short-circuits the scene and gets you your goal. Need to convince a Prince to appoint you counselor? Declare that he's actually your brother! Need to defeat a monster? It turns ou you happen to have the bane that instantly kills it in your backpack! This isn't the player being a jerk, it's what any character would do if they could in those situations, a-al the Matrix.