So many comparisons are being made with it like a warrior's sword or what have you. However it's neglected that the warrior is also using other skills! It makes for an unfair assessment.
Try this: Make a warrior who ONLY uses one handed (or two handed); no armor, no blocking, no spells and definitely no cheap alchemy/smithing/enchanting. Now when people who complain about how weak destruction is they are trying to argue one skill vs three when comparing a mage to a warrior are doing it. Is that going to be easy? No, but it's a much more fair comparison. You can play how you want, but there are limits to what will be successful and what won't.
With regards to spell damage not scaling with destruction skill that's a whole other issue. It comes down to you need to use those bigger spells and invest heavily in to regen magicka. I would like to see the lower level spells still be useful and scale up too. I don't think however that would make destruction any more powerful, just more dynamic and fun. It could be a bug but not likely. Since weapon skills work this way I think it should be moddable.
TL,DR: Destruction magic is just as viable as a one handed; you just have to use alteration in place of heavy armor and restoration in place of blocking otherwise your comparison is flawed.
There are just TOO MANY points I can make that say mages overall are underpowered compared to warriors that I can write a book on it. Here are just a few
1. Destruction never gets stronger.
2. Mage spells are either too weak or cost too much mana to sustain in a fight.
3. Mage runs out of mana, has to run. Warrior runs out of stamina, continues to pound heavy damage.
4. Mages do less damage than warriors AND are 10-100x less durable in battle.
5. Master level destruction spells take 5 seconds to cast, cost too much mana, and don't get stronger after you get them at level 50 while monsters get stronger.
6. Warrior late game can have insanely strong legendary armor and weapons that do 500 damage per regular swing without power swing and tank like a god, mages have the 100 damage master spell that takes 5 seconds to cast when they are vulnerable.
7. Warriors can faceroll through the game with 2 skills and two hack buttons. Mages need to constantly switch spells, run around, drink potions, use shouts, use lydia, ect just to get by.
8. Robes with magic regen/cost reduction is nowhere near as good as the armor that makes warriors unstoppable late game.
9. Warriors with heavy armor and weapons can whip out their flame spell anytime and do as much damage as a mage while able to tank so much more, mages who want to fight with swords end up getting [censored].
10. I have yet to find a pure mage at any level able to complete the main quest line, I see warriors level 20ish complete it easily.
11. A TON of people complain about destruction being underpowered and mages in general compared to warriors. No one complains about warriors be underpowered, only overpowered.
12. This is a TES game. Players should be able to play how they want. If they want to focus on destruction without much help in other magic fields they should be able to do that. Game favors warriors heavily to faceroll through the game.
13. In even decently balanced games, warriors can always tank more damage while mages do much more damage and can nuke from afar. Mage destruction spells are mid-close range spells and can't nuke while warriors do more damage. In league of legends we see spell casters like ryze who die instantly and move slowly but can nuke so well and does more damage than tanks like malphite who are very hard to kill but barely do any damage. Imagine if malphite did more nuke damage than ryze. Who in their right mind would want to play ryze then? Everyone would want to play malphite. Same thing is going on here. People play the more balanced characters and like to play by what is better. This is an elder scrolls game and people should be able to play how they like but instead are forced to be melee or struggle through as a mage.