The problem with Veigar is his w (solution? inside)
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Veigar's abilitys are quite unique. Q is a wonderfull farmtool and can be used to harass (a little weak for that but hey, it does something else already).
E is a powerfull ability out of lane and exciting gameplaywise (you'll STAY in that evil cage no matter what !)
The ult ensures damageoutput, his other damaging skills are skillshots, so i dont see a problem here.
For the W... It's a nuke that's 100% dependant on the stun from e. It's an old skill with massive numbers attached to it, but i think the reason why veigar feels clunky to play lies in that ability. After the rework, this feels so terrible to use. It's a ,,dead'' skill most of the time and you'll never be able to use it in lane out of waveclear purposes. Later on it nukes, but only if someone is cc'ed.
I think w is the cause for veigar's unpopularity. Dont get me wrong: I think balancewise veigar is quite alright, maybe on the weaker side, but the w takes a lot of fun from him.
MY SUGGESTION:
Rework the skill. I like the idea behind a meteor falling on my enemy but decrease the impactdelay. A little bit slower than a kog'maw ult should fit. Then give him a chargesystem like vel'koz' to store 2 at a time. Then decrease the manacost and increase the cd. Lower the damage A LOT (something like 60/90/120/150/180 +60% ap) , keep the current castingtime.
The result would be a fun minigame inside the cage of doom, where veigar could send 2 meteors to hit an opponent, using the cagewalls to land the strikes. His waveclear wouldnt be increased because of the decreased numbers, his poke would be more reliable but also still very dodgeable. His burstcombo would suffer until he put some points into e but then it would be similar to the current one. Through the higher cd, there wouldnt be a problem with a spellspamming veigar, he just gets the chance to split his damage as he likes once.
This could make veigar a superfun champion and make him much more reliable. Thanks for your time!
Edit: There seems to be a misunderstanding that this change would destroy his burstmageidentity. But as long as the stun has enough ranks, 2 w-charges could be landed on the same target dealing slightly more damage than the current nukeversion.