(AP Ratio Item) Veigar Build- Is It Worth It or Not?

Veigar is a champion with infinite AP, so I have to ask if you all think a build that completely abuses this fact would be good. GLP offers a 100-200 (+35% AP) magic damage boost, Lich Bane offers a 75% Base AD (+50% AP) magic damage boost, and Luden's offers a 100 (+10% AP) magic damage boost. This adds up to a total of 200-300 (+95% AP) (+75% base AD) magic damage boost to add to your burst and GLP adds you a slow to make setting up cages a little easier. Without runes, the build only reaches 30% CDR, but this can be fixed with runes. What do you guys think of it?
EDIT 1: Second Build

Based on feedback, I edited the build to this.

.