That 30% does nothing when you look at all the enchantments you can have on your equipment later in the game. Even restoration gives 50% extra regen. I play a sneak mage, because I selected a dunmer, which is basically that. Besides I wasn't complaining. You are complaining. What you're saying is "don't use skills to make your character more effective and see how that works!". The game doesn't use classes, but if you truly wanted to go there, sure an armorless vanilla mage that can't figure out which end of the blade goes into the enemy is weaker. Yup.
I had no reason to assume you're using enchantement. You didn't mention it in your first post and not everybody goes for the zero mana cost. Anyway, it's a long way before you're able to enchant your gear with -100% mana cost, unless you're grinding.
You say mages are overpowered. They're not. They have three sources of damage: Destruction, Conjuration and Frenzy (or whatever that spell is called, I'm not sure, I don't use it). Destruction is broken due to no scaling, Conjuration is very powerful only when you're able to control two Dremora Lords, and you have to max out Illusion to make it overpowered. Generally, melee damage is higher and easier to deal than magic damage. A fact.
Now, the whole problem with magic in Skyrim is that's considered weak COMPARED to melee/archery. Playing a pure mage is more difficult than playing a pure warrior. A fact. What you're playing isn't a pure mage, therefore all issues associated with magic being underpower don't apply to you. What might interest you is that Sneak in fact in overpowered. But it has nothing to do with magic.
What you've observed is that a character using both magic and melee is more powerful than a character using only melee. Why would that surprise you? It's always been this way. That's why Battlemages are beasts in almost every game you'll play.
I'm not saying "Don't use skills that make you effective". All I'm saying is: "When you make a statement about mages, please play a mage first."
When comparing magic to melee, we're using typical builds: warrior that doesn't spam fireballs, mage that doesn't backstab people. One-handed and Light Amor are not in a mage's skillset. A fact. You're playing a mixed build, so you shouldn't write about magic builds.
I've played an archer, a dual-wielder and a pure mage. The mage was the most difficult of them. Places that my archer cleared with barely any effort, my mage struggled with. Even after I installed Better Magic mod, I still feel my mage is less powerful than the rest of my characters. I imagine it will stay this way until I max out Conjuration and have two summons tank for me.