"You start casting blizza.....?"

[Airget]

The three elemental spells have their own unique traits, rather then being carbon copies of one another they work in the following fashion.

Blizzard is a non combo skill set in which you are always granted it's additional effect, the advantage is you don't have to cast it in order to arrive at the enmity down Freeze effect but you don't gain the perks of performing a combo aka no mp cost.

Thunder is a 4 step combo leading to burst to allow for strong single target dmg.

Fire is the AOE 3 step combo. (minus Flare)

It would appear the reason why blizzaga was left out is because blizzard doesn't combo so rather then cut off the combo of fire or thunder they decided to cut out blizzaga.

-Edit-
They wanted both mage classes to have at least 2 combos, I guess giving them three may have been a little to OP but since Flare isn't part of the combo they had to compensate by adding in firaga before blizzard otherwise THM/BLM would only have a 4 step and 2 step combo