True, though the places I lived in California (Sacramento, San Luis Obispo in particular) all had eaves. Covered patios were common too.

I feel eaves are more to keep the drip line from rain from hitting the foundation than for any heat abatement. Typical spanish style roof will not have anything on the side that isn't sloping for example. Just sort of ends flush with the wall. Some don't have any eaves at all really.