The underlying problem for veigar.

There are many, many better zone mages (Azir? Orianna? Zyra? Heimerdinger? Hell, Morgana?) and just as many catch mages (Malzahar? Again, Morgana? Ahri? Cassiopeia? Syndra?). If you'll notice, all of those zone mages do damage in their zones AND have CC (or the threat of CC) to go with. All those catch mages have great damage if they caught you, and all of them have an easier time catching then Veigar does (and they actually do something before catching someone).

Veigar is a massive burst mage, except he has a horrible early game and his entire kit relies on either enemy idiocy or teammate high duration hard CC. His only guaranteed damage is R, and unless an enemy is stupid enough to stand on E's side his W and Q do not exist. Sure, lategame he's massively powerful (assuming teammate hard CC you can capitalize on), but his W and Q will not land even on a caged enemy (because they have enough room to easily dodge all of those, and if you get closer to guarantee Q hits they'll just nuke you).