Water tanks and storm water drainage

Would water tanks on every home reduce the need for storm water drainage? Thinking about it briefly, it should mean that whatever water is running off the roofs of houses is being trapped in water tanks and not running down the street. Then again, you'd still need to account for the kind of storm that fills every tank to overflowing, which means you need full capacity.

Mokalus of Borg

PS - And on the whole it's probably not worth taking into account.
PPS - It may become more relevant as time goes on.