I'm too lazy to do this so I'll just sum up a few of many reasons why veigar would make a great support.
A huge misconception of veigar is that he REQUIRES farm to thrive, this is untrue, the bonus ap he gets from his q is just a HUGE bonus to his stats and getting assists allow you to get ap in additional to the farm you're going to be last hitting with q due to relic shield. To add on to this, try to always farm with q and ALWAYS get the cannon minion with your relic shield.
Back to the main point, veigar isn't like a normal damage support because in this case we're building him tanky, but instead of being just tanky, he also does huge amounts of damage from the already explained passive of his q. Thats the main thing about tanky veigar, he can't die yet he still does TONS of dmg.
His w just provides even more damage as it has great scaling and zoning in small areas or in teamfights forcing your opponents to move away and timing it with your e to make it even more impactful.
I just assume that veigar's e is one of the best zoning abilities in the game, if you're caught inside, people tend to not be able to get out as they dont want to get stunned (Unless they have a blink but not many do). This forces people out of fights as they can't leave the area or it'll just provide a 2.5 second stun. AND THIS HITS ALL OF THEIR TEAM if used properly, the amount of efficiency that could be gotten with this one ability is insane. With the 40% cdr you have, you'll have it up every 8 or so seconds, and it lasts 3 seconds so the enemy team will only be in "full control" every other 5 seconds.
And last but not least, his R is insane, even though he's tanky, his R still has one of the best scaling ap rations in the game and it even SCALES OFF OF OPPONENT AP, this just means that 80% of their ap is dealt to them as damage. This is a huge burst tool that can be used to zone in many situations since you are tanky, you can walk up to their apc to zone them because if they don't back up, they risk a potential veigar ult heading straight up in their face.
So to sum everything up, Veigar is just a spectacular support and if you build him tank, he's the tank that does TONS of dmg and takes none whilst peeling and zoning for your whole team.