I'm level 30ish pure mage and just rolling through people. At one point I thought I had made a mistake, but then I read a post elsewhere about how to make sure your mage takes no prisoners.
My destruction was also lacking because I ended up becoming a conjur/resto mage to survive. But then I did what's below and am tearing it up.
One thing that helped (didn't believe at first) was that Magicka regen is far, far, far less important than the bonuses that reduce the cost of spells. Your magicka will regen like crap in combat no matter what. However, if you have a good amount of reducing benefits, you can cast and cast and cast.
The main step was getting enchanting to 100. You want the 5/5 initial benefit, Insightful enchanter, Corpus Enchanter and Extra Effect perks.
You'll want to disenchant something with a destruction bonus on it to get Fortify Destruction.
Enchant a ring, circlet and necklace with Fortify Destruction. Once you're at 100 enchanting, these pieces will really rock.
Put your perks for Destruction into Shock 2/2, the usual adept/etc, Dual Casting and Impact (nice).
For leveling, keep choosing Magicka until about 300-350 base then go health. Also, get health on 1-2 pieces of your gear.
Get the spell Chain Lightning. Dual cast it to send your enemies into oblivion. Once I did these changes and started dual casting, my destruction took off. Took me like three days to go 50-51 before this. After, I went to 75 in a handful of hours.
Should point out that the Impact effect works on dragons. Without any real magicka regen on me, I'm having no trouble. Took on 8 guards at once last night and the battle lasted about 30 seconds I think. My magicka bar was still plenty full for more.
In short, do your stuff right and being a pure mage is plenty fine for blowing through stuff. BTW, my armor is the arch mage robe and some 0 or 1 armor items. Don't need it.