I've lived in LA ~12 years in a couple of different apartments. In all my apartment hunting I've never encountered a unit that doesn't come with a refrigerator.
My friend moved into one two months ago that had no fridge. I've seen a handful of similar units. Perhaps it's the price bracket you're looking in? These are often cheap apartments.
I lived there for 9 years, and moved nearly every year (7 times in total) and always had a fridge provided, it never crossed my mind that a place wouldn't have one.