Yep, more spell combinations would be great, but they would not help to differentiate mages, because everyone could use them.
Not reasonably. Because if you're running an assassin, you wouldn't want to spend 8 traits/levels in order to learn (to use my example from earlier) Fire 4 and Earth 4. You'd end up with a crippled assassin who misses some good assassin traits, and can cast spells without getting the benefits of the mage path, or the evoker trait. Don't misunderstand me: I'd like to see more mage-specific traits. But I don't want to see non-mages hobbled by removing their access to spellbooks. The player should determine how they want to develop their champions--and if that means piling spellbooks on an assassin, well, it'll be a less effective assassin, but it's their choice.