LLC annual registration is up to $800/yr in CA, including foreign LLC's. I don't think $800/yr for privacy is a "very tiny". Not to mention you would need to pay an owner of record, probably a professional, to have their name on the LLC.
EDIT: A quick web search shows that an estimated annual cost of $50-$400 for a registered agent in CA. So the cost is closer to $1k/yr.
I have an LLC registered in Nevada. I neither live there, nor do business there.
Most states allow for this - I don't know about California, though.
Living in California is expensive in general. Average LLC costs in the US are under $100.
> Not to mention you would need to pay an owner of record, probably a professional, to have their name on the LLC.
Whether that is public record depends on the legal requirements in your state. And in any case, costs for registered agent services are typically comparable to the costs of an LLC.