Yeah, that's solid advice. One thing I'd add - don't sleep on the perks that boost specific damage types. Like, there's the frost damage one, the fire damage one, the shock damage one deeper in the tree. They stack with Augmented, so if you're committing to, say, frost as your main damage type, you can actually get a decent multiplier going. Pick one element and lean into it rather than spreading yourself thin across all three.
Also, Dual Casting is honestly the game-changer here. I didn't realize how much it mattered until my second mage run. The perk effect triggering twice (so Impact staggers way more reliably, or whatever your perk is) changes the entire feel. You go from "I'm tickling enemies" to "I'm actually controlling the battlefield." It's not just damage - it's utility.
The other thing nobody mentions: your positioning and spell choice matter way more than they do for melee. You're not wrong that Destruction feels weak if you're standing in the middle of a group trying to burn things down. Kite backwards, use Impact to stagger clustered enemies, grab a summon from Conjuration if things get hairy - destruction works better as part of a toolkit than as your entire offense. That said, if you want pure raw damage with less fiddling, yeah, Conjuration or Alteration are easier carries.
Magicka regen is probably your actual bottleneck though. If you're chugging potions every 30 seconds, no amount of perk optimization helps. Throw some Magicka Regen on your gear and see if that makes it feel less like a chore.