The problem is not to do with the 'power put back' being 'larger', it's to do with efficiency. If charging and discharging a battery were 100% efficient and the

The problem is not to do with the 'power put back' being 'larger', it's to do with efficiency. If charging and discharging a battery were 100% efficient and there were no losses to heat through the rest of the system, then there'd be no discharging, but, yes, due to the laws of the universe, this will always cause a net loss.