I would say yes, on average, this is true. I lived in California for 4 years. I was paying around $1600 a month for a very tony apartment. When I moved back home to be closer to family (In Pennsylvania) I got the same size apartment, probably slightly bigger for $450 a month. I noticed tech items also cost more there as well. Like a phone I can get here that costs $500 will be $900 in California. People always talk about raising minimum wage state wide but the cost of living would go up everywhere so it wouldn't be like you were actually getting more money, the government and states would be though because it is more they can tax from people.
Yup! Having living in NYC for 4 years, I can tell you that unless you are already wealthy or you have a very good paying job, you won't be able to afford much. It is not like they showcase it in Friends. You need to earn a good $4,000 a month to be able to afford anything larger than 500 sq ft studio.
I never lived in a state where this was the case but based on what I see online and in social media, most people in these areas complain about unfair wages and the cost of living being too high even though they have a minimum wage of 15 an hour.
Most people I know who live in these areas have worse credit because the cost of living is substantially higher and it forces them into taking out lines of credit just to get by.
California is so expensive which is why you see such a wide gap in income. There's lots of rich people and lots of poor or homeless people. I could never live there.