The Santa Anas blow west OFF the desert, bringing dry air and strong winds, but the coastal areas of Southern California are simply not deserts by any definition. It’s the same climate as the Greek and Italian coastal areas. Are you going to tell everyone that those are deserts?
Death Valley and Maricopa are in the desert. Santa Barbara and San Diego are not.
1. The Santa Ana winds do not merely blow westerly. Their direction depends on where you are relative to the high desert area. Yes, if you are more coastal above the L.A. basin, they come mostly from east of there. But if you are out in the “Inland Empire” or even some places between there and the coast, the Santa Ana winds come down from the north through available mountain passes (like the huge Cajon Pass north of San Bernardino. (I know, I grew up there.)
2. O.K., Santa Barbara might not be a desert, but it is dry more of the year than Greece or Italy, both of which have annual average precip much greater than Santa Barbara, as is true for a good amount of the coast of SOUTHERN California; which I have always heard referred to as semi-arid in climate.
Southern CA is not a desert? Turn off the water supply for 1 year and I can assure you, you will see a desert landscape.
Nearly everything growing in S. CA was planted by people and if the water is turned off, most if it dies off very quickly.