Compared to drinking 5 gallons of fortify restoration and smithing followed by equiping a "lulz armor of endless enchanting".

yeah.... its weak....

Like when utilizing 100% cost reduction and impact stunlock?

As far as I remember, Destruction has incredible magicka cost which doesn't justify the damage dealt (or maybe it's the other way around). When taking into account the amount of time needed to regenerate magicka without any magicka potions, yeah it's underpowered

And when you pull the magicka potions out, someone pulls the vegetable soup out

If you abuse stun-lock and reduce magicka cost to 0 (or any other amount where you can freely spam spells without having to worry about magicka reserves), then yes, it is overpowered.
However, it is also dull and makes you feel cheap instead of powerful.

Bethesda should've made damage scale with improved Destruction skill instead of reduced magicka cost AND put a limit to a maximum magicka cost reduction (20% seems fine).

The whole take on magic in Skyrim is horrible, actually.
Everything is either overpowered, underpowered or dull (there might be exceptions I overlooked, though).

Also, did Bethesda fix teleklinesis?
That's one spell I can think off that has absolutely NO usefulness at all.

And no, I won't mod it or use mod for that since it's Bethesda's job (mods should be used only to add on to existing experience, not to fix it).

I don't utilize, nor have I ever felt the need to utilize, 100% cost reduction. I use stunluck, sure, but it's not nearly as useful as people seem to think it is. It doesn't work everytime guaranteed, and when you are facing multiple enemies, which is the case quite often, you can't rely on it.

Using one hand weapon with Ignite in the other hand is an extremely effective combat method on alot of enemies.

You fire poison with ignite which slow burns the enemy (and this spell stacks!!!!) and hack & slash with the other hand. job done.

You should be fine, as long as you up that cost reduction. 30% will get you nothing. You'll need at the very least 85-95% depending on which spells you use

Alternatively you can boost up your magicka regeneration. That's what I do for the most part and I have had no problems playing mages.

Ah, another generation of the destruction is weak question. Might as well add my 2 cents:

If you really just specialize in Destruction, and a little Enchant for cost reduction, you'll top out at level 25 or so and at that point Destruction is not underpowered at all even at higher difficulties. I think this a valid way to play even though I completely understand that some will find it boring to stop level progression.

If you want to get to high levels, that necessarily means you'll have to develop other skills. It's these other skills that will keep you strong in conjunction with Destruction. It's simple, take your choice.

Actually, a pure Destruction mage is a very fun and enjoyable playstyle, quite different from anything else. It has its challenges, but it's definitely doable.

Caveat: I play on Adept, so I can't comment on the higher difficulty levels.

People on these boards often say that "you can't use one skill alone". If you try it, though, I think you'll find it works quite well. If you are truly focusing on Destruction and not working up other skills, you will be very powerful compared to the foes you meet at your character level. Remember, the game world scales with you, so if you're getting lots of other level-ups from things like Sneak and Conjuration and Illusion, your Firebolt will seem like it's doing less damage against the higher-level foes you meet. But if you keep Destruction as your strict focus, you will be very effective.

Destruction magic has a lot going for it, despite the fact that the spells don't scale in damage. You can put out more damage faster than an archer or warrior, if you get good at double-casting. You don't have to account for trajectory when aiming, like an archer does, so you can easily hit things from very far away. Since you're most likely wearing robes, you can move quickly to stay at range. And you're the only character in the game who can hit multiple targets at once (except for a 2-handed warrior who has taken Sweep, and that is sloooow!).

Magicka cost is high for Destruction spells, but if you focus on Magicka instead of Health, you'll have enough. (This also makes you feel like a 'squishy' mage, which makes combat fun IMO instead of a boring slashfest with a fully-armored warrior who has a godly health pool.) You can buy or find Fortify Destruction and/or Magicka Regen gear, so you don't have to work on Enchanting. I've played several 'pure' Destruction mages like this and never got 100% reduction.

You'll want to use tactics to preserve your Magicka pool during battles. You don't need to sneak through dungeons - just walking slowly will often give you enough of a warning about foes who are ahead. Drop a dual-cast rune near a door if you're concerned there might be foes ahead. The rune will do something like 100 points of damage when it goes off, but until then you're letting your Magicka regenerate to full, so when you *do* need to go in blasting, you've got enough blue to blast with. When that rune gets triggered, it just did 100 points of *free* damage. People complain about rune spells being weak, but hey - 100 points of damage for essentially no cost sounds good to me!

The OP didn't specify wanting to play a 'pure' Destruction mage, though, so I should stop prattling on about how fun it is. Suffice it to say, the "you can't use only 1 skill" argument hasn't been convincing to me. Used in combination, as the OP plans, Destruction can give some new tactics in battle. Of course, since you're not focusing on it exclusively, you'll probably find that the spells are more expensive than you want to deal with - but then, that's why you have a sword in your other hand!

Underpowered? Compared to a fully smithed something with uber enchantments etc etc then probably. Compared to bare fist fighting, then no.

The skill system of the game works as a process, not stand alone singular skills.

Do what you want, try things out, have fun...don't pay too much attention to what people tell you. It's a single player game, you aren't in competition with anyone.