I'm also a little concerned about the proposed shard requirements (maybe for nothing, though, as we don't really know how stringent the requirements will be, or how broad).
But I would like a system where the majority of spells can be learned and used by anyone with the appropriate magic books (possibly modified by some randomness - don't really know where I stand on that). But in addition, the more shards you have the more powerful your spells of that type (or partially of that type) become. So IMO, many spells should have no shard requirements. Some spells should require X shards, but of any type. Other spells, but a minority, could require specific types of shards. I think such a combination would work quite well.
Additionally, possessing more shards than you need to cast a spell could boost the spell's power in some way. For spells that don't require any shards or don't require specific types of shards, this bonus should be relatively small. For spells that do require specific types of shards, the bonus should be larger.
What would make this even better is if you got to choose how that bonus is manifested. Let's invent a spell called Meteor Shower (not particularly original), and pretend it requires 2 Fire Shards and one Earth Shard. You possess 3 Fire Shards and 3 Earth Shards. This allows you to increase one "fire" attribute of the spell by one "interval," and up to two "earth" attributes of the spell by up to two intervals at most.
For example I could choose to increase the fire damage of Meteor Shower by A%, or the explosion radius of each meteor by B%. Simultaneously I could increase the physical impact damage by C% and, say, the total area of effect of the spell by D%. Or I could increase the physical impact damage by 2C%, or the area of effect by 2D%. Alternatively you could simplify it and not distinguish between having extra earth shards and extra fire shards and allocate your bonuses accordingly (so if you have 3 extra shards of the relevant types, you could improve up to 3 attributes of the spell by a total of at most 3 times).
You could have the spell cost increase for each allocation, so if you're concerned about mana you might not want to allocate all, or even any, of your 'bonus points' to keep mana costs down. The greatest thing about this feature is that it'd make spell-casting feel very personal - so that even when using generic spells, if you have enough shards of the right types you get to alter it a little, making it feel that much more your own. And, it could be accomplished easily with a straightforward and simple UI - you could even allow us to save defaults.