Why should a fireball with 80 destruction hit harder than an arrow with 80 archery? Or are you saying you die far quicker than an archer in armor? In which case I would reply to you, that archer also has some sort of armor on (which just so happens to be a skill). Maybe level up your alteration and restoration if you're dieing so quickly. Armor/Health spells are just as good as armor/health pots.
A fireball with 80 destruction should hit harder than a bow with 80 archery because:
You can’t smith your hands to launch fireballs harder
You can't enchant a fireball to do more damage
You can't poison a fireball to do more damage
Even ignoring these arguments, fireballs currently do LESS damage than arrows and, by this same logic, why should an arrow with 80 archery hit harder than a fireball with 80 destruction? Well according to the current mechanics it should and does.
Your destruction skill has no effect (yes, NO effect) on your spell damage, where archery skill increases arrow damage
Destruction gives access to perks for 150% damage, archery gives 200% PLUS 30% crit chance
Notice I have yet to use the argument that a mage dies more quickly, though I will say that no, alteration/restoration are not as good as armour/pots. The 'skin' spells do not give close to the armour of equally perked armour (50% reduction tops as compared with even light armour which can hit the cap of 80%) and again, cannot be improved. They also have to be recast every minute which eats into your offensive power. The final armour spell which does give capped armour (and makes three perks obsolete) has to be recast every 30 seconds eating even more magicka! Same goes for restoration, no other skill group needs to use it's main offensive resource for defense and utility as well, meaning that a mage using all of these skills will also need to use pots to replenish their magicka.
Having said that, I personally don't believe that squishiness is a valid reason to give destruction more damage than archery, I stick with my first three above and will throw in that I believe impact is a poor excuse to balance it out which should be nerfed down to 60-70% chance to stagger (higher than the archery perk, as this is the only utility given to spells where bows have 15% stun on top of slo-mo and bash). I do however think that they are reasons to buff alteration to be able to give armour cap if perked to the same degree as light/heavy armour, can’t comment heavily on restoration.
Simply put, create two characters with equal defense/utility skills and with equal perks in damaging skills they should do similar damage. This is not the case, not by a longshot, and THIS is the problem with destruction. I don’t care whether or not it’s viable to play destruction, I care that it doesn’t have nearly the feeling of power that shooting fiery death from my hands should give, when I know that it’d take half as many arrows to kill any given thing in the game.