This thread is funny.
You zap a yeti, he says ooh, spring breeze, nice snow storm! You zap him with a fireball instead, and his hair catches on fire. You zap a bleach blonde with a fireball, she turns over to tan the other side. Stick her in a snow storm and she'll have to invent practical clothing.
What is nice is this whole argument is tied to semantics. Fire elementals have to resist fireballs just because both of them have the word "fire". If the school with damage spells is called, for example, Chaos (that sounds familiar) and the fireball spell is called doomball (familiar too, not as much but close), or chaos storm or whatever, then suddenly, it makes sense that the fire elemental is damaged by the spell...
Or, you be a ninny, put twice the work in, and do impractical idiocy, sticking immunities and resitances all over the place, with specific spell lists or spheres of influence. You make a mess.
Mmm, at least for me, separating spell lists where chaos gets damage spells, life gets buffs, nature gets summons or things like that, looks pretty interesting. Much more than fireball, mudball, natureball, boringball and so on.
You can't really do much if you don't have different damage types, you just end up with clutter trying.
Your idea, but you can do lots of things with a generic damage type, because lots of things aren't tied to damage at all.
It's practical unless you want generic spells. A freeze effect applying to a walking popcicle just doesn't make sense.
Common sense and the physical laws of magic...