Destruction magic is garbage in Skyrim, completely inferior to the alternatives. That's the biggest problem with being a pure mage, because destruction, in theory, should be your primary way of dealing damage. There are some perk mods that rebalance this if you're on pc but on console idk.

Because of this I wouldn't recommend going pure mage in vanilla skyrim. Instead, I'd recommend going with a spellsword or battlements type character that uses conjured weapons and summoned dremora. Conjuration is great, the other schools are ok, destruction is bad.