It depends what your criteria are, but most of the LA basin would not be considered to have a "desert" climate, instead a Mediterranean climate. A good amount is intermediate and considered "semi-arid". To get to a proper desert climate, you do have to go just outside the urban area, over the mountains into the rain shadow where you'll find the Mojave desert.

The border between "Mediterranean" and "Semi-Arid" is (according to Köppen) set by a threshold of precipitation based on potential evapotranspiration, which depends on things like average temperature. Once you have that threshold, precipitation at below 50% is considered "Desert", 50-100% is considered "Semi-Arid", and beyond would be other classifications (like Mediterranean in the LA case).

Maybe this sounds arbitrary but it shows that most of LA gets at least double the rainfall that a desert would, according to the most common climate classification scheme.

Well, you were wrong. Much of the area is California chaparral and woodlands, not deserts. The Mojave and Sonoran deserts are at the far South end of the state.

California has incredible fog forests also, home of the second tallest tree species registered in the planet. A desert would not have evolved giant slugs and arboreal salamanders.

It was a much more humid place in the past, probably.

re-aridification

Ssshhh. You’ll expose the incompetence of our leaders at managing infrastructure.