If you have a better place to store them, I'd like to hear it. 
It's also a good place to store oil tankers.
I can only imagine what happens when a lift breaks in one of these car parks. Not even for damage or anything like that, just for the process of retrieving cars.
I always think of this too. And the fact that cars can leak various fluids etc that can fuck up the paint on other cars or mess with mechanisms etc.
I think this might be why these are one of those 'mostly in Japan' things because of their meticulous attitudes to maintenance. (And maybe people are more patient in general when something does goes wrong)
The tech has apparently been around for over 100 years at this point, and exists in other high density cities to some degree, but in Japan they're everywhere.