Why would one pick a mage instead of an assassin mid?

Mage=mid to long range ap champion with high mobility and high burst dmg Assasin= mid to short range ad/ap champion with high mobility and even higher burst dmg

Other than who can do dps burst dmg as mage, most other mages are still all burst champions. Assassins usually have shorter range than mages(cough cough) but their mobility will easily make up for the range difference. Why would anyone pick a mage who has no mobility and hard to get through the front line, instead of assassins who has insane mobility and arguably higher burst dmg?