LA is over 13 million, and the second largest metro area in the US. Even SF is a larger metro than Phoenix, and both LA and SF are coastal port cities. It makes sense that they should have more diverse populations, especially LA.
That's almost like comparing any city to NYC.
I still believe culturally Phoenix is more diverse than the Midwest, due to the fact that it is a "new" city - the majority of development happened after 1970. Also, it is a city of very recent transplants. This encourages innovation because our city is so new we are not yet steeped in tradition or run by "old money families".