I would actually like this a lot. It'd be nice to play through the game with multiple teams but on various NG+ settings, like the Tales series has.
And you wouldn't need to worry about an example like
>>36349186 happening. The fun would wear off quickly because there would be no challenge and no reward.
I speak from experience; when I tried playing Symphonia with NG+ and had all my weapons and skills unlocked from the start, I realized it wasn't fun.