I have 1 good reason for keeping 'tarp' covers pumped off and clean - what if the tree had ripped the cover? If you develop a hole in one that is full of debris and algae, all the work you did to clean your pool when you closed it is wasted (I think Watermom's cover blew into the pool last year and left her with a real mess this spring).
Just my $.02 - but if you pay that much for it, you're wasting money