I can't speak for California, but I know Washington actively thwarts ICE at every turn.
We declare sanctuary cities.
We
forbid our police to inquire about the citizenship of people they interact with.
Our governor made the DOL stop confirming identities through using SSNs in an attempt
to shield illegals.
Washington State made it illegal for employers to
discriminate based on citizenship.
Our governor has ordered police to make
NO arrests over immigration status.
. . . and that's just a sample, there's plenty more. I can only imagine that California is a decade ahead of us.
So ICE may have the powers you suggest, but when the local government forbids police cooperation and actively shields illegals from detection what good is it? They have the power to detain and question people, but all the people they need to detain and question are being actively hidden by the state.
That's not being at the top of the social power structure.
Having the government actively protect you from detection and prosecution, while providing you aid, sanctuary, and employment - that's top of the social power structure.