I understand if a Calif. landlord requires current car registration. Why would they also need proof of current car insurance?
In the past, landlord never required a copy of current car insurance. Now they say they must always have it on file. Do they have a legal right to require it? It is not written in the lease that all tenants sign.
The landlord probably does not have a legal right to a copy of your proof of motor vehicle insurance unless it is contained in the lease. I assume from your question that you do not have motor vehicle insurance -- which is legally required to operate a vehicle on any public way in California. It might help if you can find out _why_ the landlord wants this proof. There may be some legitimate reason for the request, or at least something the landlord thinks is reasonable. Your opinion may vary, likely depending on your own insurance status.
You may not think you can "afford" insurance, but you can't afford to drive without it. It is a traffic violation, for which the fines will quickly cost you more than any reasonably priced insurance policy. When you are involved in a motor vehicle accident, not "if" but when -- your insurance would provide two benefits. First, you would be given a lawyer by the insurance company to defend you from litigation regarding the accident. Second, the insurance company would pay for any judgment or settlement to an injured party, up to the policy limits of the insurance policy you purchased.
Finally, when you are involved in a motor vehicle accident and the other moron doesn't have insurance you will have to pay your own way -- repairing or replacing your car, paying your medical bills, paying his property damage, paying his medical bills, etc., etc. You might not have an assets right now, but later in life you might want to be able to buy a nicer car, buy a home mortgage, build up some assets or keep your lottery winnings. You really can't afford _not_ to have motor vehicle insurance.