The main problems for mages are archers and sudden attacks. You may be easily killed before you cast the ebony armor.Although this spell is weak too and does not help much. I'm using the shouts Become ethereal and Detecting aura. But not all mages can shout and detecting aura makes the game uninteresting. Besides it is inconvinient to cast spells detecting life every several seconds. Become ethereal does not help much if you are being attacked by a mixed group of archers and warriors. What to do with that unusable class created by Bethesda. You cant even scout Skyrim quietly because you have to be ready for a sudden attack. Any attacker can easily kill a pure mage with one or two strikes. Farengar says intellect is the main weapon of a mage but how intellect can help if you have not noticed the enemy first? Dragons are also a big problem for the pure mage. They do big damage so you must have a quite large amount of health to survive even one bite and keep you health at 100% during the fight keep ebony armor without it you will be eaten immediately. I would say mages are living in permanent fear and it is killing faster than enemies. For playing as a mage you must have perfectly sharp eyes (that is a rare thing among scholars) and be always on the alert.
I completely agree with you as pure mages are glass cannons. Archers and other ranged enemies are the worst.
But I disagree with you about Dragons. They are actually easiest to defeat when you're pure a destruction mage. Just use wards to defend from breath attacks, and use Impact to stagger them with fireballs, and whatnot.
"Dragonhide" is the best defensive spell. If you want to play "pure mage", you should have more than enough Magicka to cast it (and the perk in the relevant skill to halve its cost) by the time you get it after completing the Alteration Ritual Spell quest.
When cast, Dragonhide temporarily raises your armor-rating all the way to 567 (80% damage reduction).
Even with Flesh spells, a pure mage will likely have to invest entirely in their magicka when leveling up, not leaving much in the way of health. On my last mage character, by level 35+ I had less than total 200 health. So you're still vulnerable with Dragonhide, but I guess it differs for everyone.
It does differ, considering that the costliest spell to cast in all of Skyrim including DLC (in terms of base cost) is "Storm Thrall" in Conjuration; at a whopping 1,200 Magicka cost.
If that is halved with the Master Conjuration Perk, that means the bare minimum amount of Magicka you'll ever need is 600. This unfortunately means (assuming you're actually that committed to raising your natural Magicka score) you'll need to invest 50 Levels in raising Magicka (or 45 if you're an Altmer).
This is why I'd play as an Altmer anytime I wanted to try a "pure mage" playthrough in the past. And once you get the "Extra Effect" Perk in Enchanting, make sure to dual-enchant certain equipment pieces with both Health & Magicka bonuses.
And heck, you really should invest in either Light or Heavy Armor skills if you want slightly stronger enchantment effects (per the "Fire/Frost/Shock/Insightful/Corpus Enchanter" Perks). Wearing a type of armor shouldn't stop you from being a "pure" mage.
Once you get the "Equilibrium" spell from Labyrinthian, your worries about running out of Magicka should be over. One trick to decreasing the adverse Health-drain effect of that spell is by simply switching to Novice difficulty while using it (almost negated entirely if you have the Atronach Stone passive).
The only other thing I can think of that should help somewhat alleviate the burden of committing to Magicka increases is by either choosing the Apprentice Stone or Atronach Stone as a permanent Standing Stone passive (or get the Aetherial Crown so you can have both!).