I couldn't agree more with you.
I always thought of elementalists as sort of specialized wizards that deal specifically with the namesake elements and focus on those - as such they should get additional +damage to elemental spells, with each PC level.
Additionally, considering that elements actually consist of fire, water, air and earth, adding extra spells to the auto-learn list for elementalists would be lore-friendly and a clear improvement for an otherwise enjoyable but slightly limited class, that doesn't really trade those limits for advantages. Nothing an elementalist does cannot be done equally well or better by a wizard.
The ability to get spells without having to read spellbooks is nice but as a sole redeeming feature, I think it's not enough.
Class powers are nice for elementalists but they are hardly exclusive since resistances are easily obtained at the respective levels, water breathing can be obtained via items, weather effects mitigated by blankets.
Elemental storm is very dangerous if cast indoors due to unpredictability and it's impossible to effectively use it against diversified monsters with different resistances.
The spells I would see as viable for elementalists would additionally include all air and earth elements, so aside from earthquake:
Lightning bolt, mystic shovel (since it is undoubtedly related to earth), teleportation (arguably air spell) and petrification as the ultimate offensive earth spell.
I believe these should become available for elementalists, but all class spells should have more initial charges and cost a bit less, to be on par with wizards' 40% spell cost reduction for elemental spells.
At the same time, to further distinguish between wizards and elementalists, they should receive significant penalties to casting spells from other schools of magic, to reflect their narrow specialty in the elemental area.
As a last note, summonable elementals should not be random, there should be a menu to choose from the four types.
Also greater elementals should become available at lvl50, similarly to necromancer's constantly increasing list of undead slaves that eventually culminates with liches at lvl ~45 (not sure exactly).
Perhaps at the cost of 5-6 mana points, a power-adjusting greater elemental of chosen kind should appear?
I believe this would greatly improve the class without making it overly powerful and reflect its specialization in elemental magic.