Its quite easy to solve the jack-of-all-mages thing going on now. Make better spells take up more spell slots, so the best fire magic spell takes up 4 slots for example. That way you cant use it with just 1 point in fire magic, you need to invest 3 skill points, and even then you only get to use that one skill because you have maxed your slots.
I've wrote out two replies and erased. There is a lot going on in the game here. I'm not sure your suggestion is ideal, I'm not even certain we have a big problem here. To get the big spells in different classes is going to take a while to build up levels, then they will have long cooldowns associated to those spells.
If you have them eat up Spell Learning Slots to, you will have a very narrow mage, that can only do a few things really well. You best hope you aren't confronted with a situation where your mage's big spells are as useless as tits on a bore.