Why isn't Veigar Bot Carry a thing?

Mainly because not having the pushing power of an adc isn't great.

You could probably make it work for some games, but I doubt it's a great pick. Ziggs is a much better bot lane choice if you want a bot lane mage, since he can still threaten structures well.

Because you will get STOMPED early game. You'll be really, really far behind and leave your team to 3v5 while you and yur support catch up.

Veigar has no mobility so even with his retarded scaling you're better off with an ADC as the main carry since they have mobility and other self-peeling tools or kiting tools.

Veigar's stun is really good but it's even better if you have another strong carry on the team besides just Veigar.