Wizards are all specialists. They begin by learning magical rituals, which later progress to spells. In other words, the spell you learn at 1st level takes longer to cast, but by 3rd level you've mastered it.
I had thought of something similar--and may use my idea (or steal yours) if I start a new campaign. My idea was that there is a base class (the arcanist) that only goes up to 8th level. There are then several advanced classes, each of which is associated with a particular school of magic (so, transmuter, evoker, illusionist, etc.). In each case, the prerequisite for the advanced class is so many ranks in Knowledge (arcana), Concentration and Spellcraft, and the having of so many spells from that school in one's spellbooks. Each advanced class was a six-level class.
In addition, there are then prestige classes, each associated with a school, with names like Master Evoker, Master Transmuter, etc. Each of these has more stringent requirements. And each is also a 6-level class (8+6+6 = 20, this system is designed to handle up to 20th level but adding epic versions of the classes would be straightforward). In addition, there's a 6-level prestige class called the Master Arcanist. The prerequisite for this is the ability to cast spells of 4th level from three different schools. This will have required the caster to have taken two levels in each of the three advanced classes, but not to have become an expert in any. So, the Master Arcanist has the greatest breadth of spells known, but cannot cast the highest level spells.
Anyway, I seem to remember typing it all up and leaving it to collect electronic dust in some folder on my harddrive somewhere. But when I read your post I was reminded that it's there.
Dave