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.