And what's wrong with one teleport spell, instead of two, for example?
Well I could be mistaken, but aren't they different effects... One teleports the caster and his army, the other teleports all unstationed units.... quite the different outcome in most cases.
or the fire bolt vs, the death spell bolt
So are these... quite similar but some subtle differences. Flame dart will get stronger as you procure more fire shards... Shadow bolt doesn't but gets stronger with the caster level and also reduces spell resistance.
One of the problems with your suggestion (and it was the same in AD&D) is that the same spells get picked over and over again... it's no coincidence you mentioned fireball and lightning bolt... they're pretty much the first spell everyone is after!
Not sure what edition/variant it was but I always preferred the AD&D magic variant where you could chose one (or two?) preferred schools/types such as evoker, illusions, enchanter, divination etc. That's a similar concept to choosing the element specialties ala FE which I think works mostly ok the way it is.
Having said that, yeah I think the bases system is fine but I think there is some scope for having certain "special" spells become available on level up. For example, maybe in addition to the base spells... if you have the Fire school then on level 5 you have a chance to be able to select the "Fire Specialist" ability or similar which unlocks a couple of extra fire based spells (similar to Book of Flames tech or whatever it's called).
I'd also like to see more rare spells unlocked via quest loot, eg "Lost Book of Flaming Explosions" which grants a couple of extra fire based spells but is only usable if you already have Fire1.