Why is lux ult cooldown so short?

I recently crafted lux's elementalist skin and so started playing her. I still can't figure out why her ult cooldown is so short when it has an aoe of like 6000-9000 square units and while relatively narrow it has a huge length. With 400 ap and 45% cdr her ult will be putting out over 800 damage every 27.5 seconds (13.75 if she kills someone).