Proposed Solution: Alchemy and Enchanting.
Case: Now before you call it exploitative, let us anolyze the mana cost of a sample of expert and master tier spells.
http://www.uesp.net/wiki/Skyrim:Destruction_Spells
Thunderbolt - A Thunderbolt that does 60(90) points of shock damage to Health and half that to Magicka, 294 base, 125 perked + archmage robes, 300 dual-cast
Fire Storm - A 100(150) point fiery explosion centered on the caster. Does more damage to closer targets, 1222 base, 519 perked + archmage robes
The mana pool difference between the Apprentice mage and the Expert mage is a couple hundred at most. My mage at level 45 does not even have enough mana to cast a single firestorm.
I hope this example has convinced you that Enchanting is a necessity in order to scale your spell casting at higher levels. I hold these trues to be self evident.
Starter's guide for enchanting Fortify
There are 4 items that can be enchanted with Fortify
I for one will choose to stick with the Archmage robes because they just look too cool to stop using, so that leaves me with 3 places with which to enchant
100 Enchanting: 10% less mana usage.
w/ 5/5 Enchanter: 20% less mana usage.
w/ Insightful Enchanter: 25% less mana usage.
w/ Non-exploited Enchantment potion: 27% less mana usage.
w/ Exploited Enchantment potion: 29% less mana usage.
EDIT: For a 27% Fortify
So if we do the math on the different levels of improved enchanting 3 items + Archmage robes, the resulting percentage of base mana use percentage:
100 Enchanting: 27.5%
w/ 5/5 Enchanter: 12.5%
w/ Insightful Enchanter: 5%
w/ Non-exploited Enchantment potion: 2%
w/ Exploited Enchantment potion: 0%
As you can see, we must use our enchanting, but we must also use self-control, for getting your mana costs down to the right amount is a delicate balance, and is really left up to your personal preferences on how often do you want to chug mana potions.
It is possible to achieve 4% (with 25/25/27), 3% (with 25/25/29), and 1% (with 27/27/29) as well.
Personally I find anything less than 2% to be exploiting and not fun, but if you exploit to achieve 3% I think thats perfectly legit, I mean what the hell your using MORE mana!

I personally think the sweet spot is between 5% and 3%. Less than 3% uses such an insignificant amount of mana that it just isn't fun anymore. More than 5% and you'll find yourself emptying your mana bar to burn down a common enemy. If you're an alchemist and enchanter, play around with the combinations until you find a balance that you like. My goal is to have my expert level bolts consume 11 to 16 mana, somewhere in that range.
Its a pretty easy choice if you don't want to level alchemy! But theres some irony there because you'll need more mana pots than the alchemist will. :\
Scaling the effect of your spells:
So now that you're using the appropriate spells at a appropriate mana cost. What about damage? What about dragon priests resisting pacify? What about Dragonskin's meagure duration?
This is where you want to be an alchemist, because the only thing that ups your damage output or duration of spells are potions, and alchemists make the best ones by a long shot. I'll let the pictures do the talking, just the relavant potions:
http://i41.tinypic.com/2a6jlmd.jpg
Also a before and after shot of Thunderbolt damage with a destruction potion: (I don't have my destruction spells perked btw thats why the mana cost is a weird amount)
http://i40.tinypic.com/2dme42b.jpg
If you want to make slightly weaker potions then only wear the 25% alchemy gear.
This helps with many things mage related beyond damage and healing. This would allow you to summon creatures that will last the duration of a long fight, would allow Dragonskin armor buff to last the full duration of a long fight, boost destruction damage through the roof, allow your illusion spells to work on higher level creatures, etc. Alchemy allows you to be a much more diverse mage without having to be a fully invested master of every school, you can happily stay an adept at something and still be extremely powerful at it. Even destruction, if you didn't want to go expert tier and only want to use it as supplementary damage, chug a potion and do more damage with firebolt than you would with incinerate. So you can see that alchemy is a very important and extremely powerful tool.
Uhm, thats it really. Lower your mana cost, use your expert and master tier spells, and in those tough spots where [censored] just needs to die fast, use potions.
Hope someone finds this helpful. I'm not saying that the spell system isn't weird and kind of dumb, but by no means is it weak. Ideally you could effectively use spells without combinations of enchanting and alchemy but thats for an ideal world.