California tried this, it didn’t work and repealed it after 10 years.  During that decade of litigation, the number of claims and the handling costs skyrocketed, increasing bodily injury premiums 32-53%. After the repeal, the spikes in lawsuits and premiums declined dramatically. 

Source: RAND Institute for Civil Justice 2001 

Washington does not have any similar legislation that allows frivolous third-party lawsuits.

After adjusting for inflation, losses have increased 20 percent in Washington for the major property lines of insurance following passage of a law allowing additional first-party lawsuits. 

Source: SNL Financial, 2007-2015; inflation adjusted by PCI 

Montana allows a third party to sue your insurance company, causing Montana consumers to face higher auto insurance rates than all surrounding states. 

A 2011 study by the Insurance Research Council found that after the West Virginia State Legislature enacted reforms to reduce third-party litigation, underlying insurance coverage costs were reduced by approximately $200 million in the five-year period after the reforms were enacted. 

Source: Insurance Research Council, 2011