Sunlight can affect chlorine. also, it helps keep out bird droppings, leaves, dust, pollen, bugs etc. An uncovered tub is also a saftey issue. I would imagine you might also have significant evaportion?
Here in New England, the summer gets to hot 80-90s, but even at those temps, I keep my tub at 98 and still need the insulation. otherwise , it will be trying to cool to ambient temps.
There are several types of covers, and not all of them are "insulatiing covers" Check out Dr Spas site
http://www.rhtubs.com/covers/cover-index.htm for differnt types of covers if you think in the summer you don't want to have a heavy insulating cover.