The problem is the destruction school was designed to be used with the other schools of magic making it very weak on it's own.Mages only have two perks for increasing damage excluding necromage which is only useful against undead.Heres a quick comparison of how a sword and board warrior and a mage can increase their damage.
Mage
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Two elemental perks for Fire,frost shock. - 50% increase
Spell type - adept,expert etc
Potions.
Warrior
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Weapon type.
Weapon skill.
Weapon quality - smithing
Critical damage.
Weapons with elemental damage effects.
Perks - Armsman 5 ranks - Savage strike etc
Armour/ring/necklace - increasing one handed damage.
Potions
The scope for mages to increase their base damage is tiny when compared to what a warrior can achieve,they can only reduce cost through items and enchanting.When mages are having to spec for 90% cost reduction at the expense of everything else then theres a problem.
Do you not see how you contradict your argument, melee NEEDS to be used with smithing and good armor for it to be effective. To use melee you have to be right up in the enemies face, where they hit like a train on master, destruction and archery can be used from range, so you can get away with no armor using destruction (I do).
You see if you can hit for 220 damage in one hit without ANY smithing using melee like you can destruction, the problem with this scenario is that the costs for dual casting an expert spell are absolutely huge. There is the real problem, magicka cost, not damage. I imagine you can hit 220 damage with a 2h daedric war hammer (which are incredibly rare) but the stamina cost is enormous, also hits at a much much slower rate than destruction.
Let's say a draugr deathlord, they have the equivalent of ~1400 health on master, I believe the highest you can get a daedric sword (which again, are very rare) without smithing is 72 damage, resulting in 20 hits to take one down (or 7-10 power attacks depending on perks).
Now dual cast incinerate deals 198 damage (220 with the illusion perk), resulting in ~300 damage given the weakness. So 3/4 dual casts (you also have fire damage) will take down that deathlord, from a safe distance.
Destruction is not weak, this thread was never about comparing the two, it sort of is now. My main point is that destruction does enough damage for you to use it well on master.
If you want to deal huge numbers with destruction with potions and poisons you can hit for over 1500 easy, but you don't need to.