A lot of the champs that were frequently banned (Brand, Veigar, Lux) have now been adjusted, making them more fair to play against.
A good case of Riot completely missing the point.
Veigar isn't unfair because his damage needs trimming. Guess what? Full tank Veigar is actually pretty good in ARAM. Veigar isn't fair because he has a shortish cooldown AoE stun that covers almost all of the lane. You have to completely and totally change how you play to deal with it, and a lot of champions don't have enough in their kit to really do it.
Riot wrote this big long post about how they understood how not having reasonable weaknesses mattered and how they'd think about it in the future. They then completely ignored everything in that post and pretend that its all about having the right Win% numbers (see discussions from Riot on Riven and Vayne). It's the classic fallacy where things that are (easily) measured matter and things that aren't as easily measured don't.
Yes, you can trim Veigar's numbers so that he is close to 50% winrate. Congrats. But that doesn't matter - he would make the game vastly less enjoyable for 5 people even if he was at 40% winrate because his kit is broken on ARAM.
This is fair feedback. Let me see if I can elaborate some, though I know it won't be enough.
Long before I worked at Riot, we tried to balance TT by changing the way specific champions worked in that mode to be different than how they behaved in SR. It made the game a lot more confusing when you swapped between modes, and was deemed a failure and something we shouldn't do again. So for years we left the side modes alone so that when you played a champ in ARAM/TT, it behaved the exact same as SR. (Yes I know there's a few exceptions, but for the most part this is the case.)
So fast forward to NB/ARURF. We wanted to make the mode more fair so that it wasn't "decided at champ select", but we had the constraint of YOU CAN'T CHANGE HOW CHAMPS WORK. It's fine to disagree with this constraint, but this is what we feel makes the best experience as you play all of League of Legends. So we tried just numerical adjustments (+X% damage taken for example), and saw a pretty decent success. Win rates became more balanced! Now it didn't eliminate the "bullshit" moments (You ever lane vs Morg + Lux in URF?), but did succeed in making it more fair overall.
So yeah, Veigar is a great example of what we can & can't solve. With Veigar on ARAM, the first nerf I applied was actually +% damage taken, because you're right that the amount of damage he does isn't relevant, but I wanted to reward players who finally caught him, that he was more likely to actually die! It wasn't enough, so I also reduced his damage.
And you're also right...I could probably cut his damage IN HALF and he'd STILL BE GOOD. You'd actually probably build him pure CDR/Tank and he'd be an amazing support for the team. That's just kind of how Veigar is designed...
That being said, it's possible there are some other levels we could consider tuning. Stun duration (Veigar)? Silence duration (Fiddle)? Shield power (Sona)? Mine Duration (Ziggs)? Though I admit I'm a little cautious about those levers since they will change how a champ feels. But if it becomes necessary, we can discuss it.
Hopefully this was helpful.