...pure mage (which means no potions, except for restore magicka ones, and no using any weapons at all) ...
To me, that's not a Pure Mage, that's Pure Stupidity?. To my way of thinking, a pure mage is one who primarily relies upon magic to deal with the world, which little use of weaponry or stealth. Not using health potions if you have them is just ridiculous. If you can brew them, use them.
Personally, I find magic a bit too weak. A warrior can make normal attacks for hours without ever using any stamina, and an archer can fire arrow after arrow for days at a time without ever using stamina, but unless you've made a lot of specific gear, any spell you cast will cost mana. (Sorry, but I generally refuse to type out the word magicka. It's an unnecessary complication). That can cause problems. On PC, I use a mod that causes destruction magic to level up with the skill, which helps a bit, but running low/out of mana is still a serious issue. It never seems to affect the enemy, though.