I kind of doubt that all the gang and drug related killers in Chicago, which are all usig guns that are illegal to possess in Chicago, would bother getting insurance policies for the illegal guns that they use to kill other gang bangers.
You've profoundly missed the point of this legislation and gotten its purpose complete backward.
They're not expecting gangbangers, drug dealers, and junkies robbing liquor stores or homes or cars to voluntarily insure their weapons. They're holding the legal federal firearms licensees from gun shops and gun shows and the legal private gun owners who are the source for the vast majority of the guns used in street crime responsible for the illegal sales they make to underage kids, felons, the mentally ill, people seeking to avoid background checks and get a gun immediately, people who are obviously buying the weapons for someone else, etc.
Most illegally acquired or irresponsibly used guns are purchased or taken from legal gun owners and licensees, and a smaller (but still large) number are stolen from them. This puts some liability on the gun owners who are deliberately reselling or giving out their guns illegally or those who are extremely careless with their legal guns, rather than only prosecuting the criminals who commit the final crime.
Read this for the legal sources of most of the illegally used guns on the streets:
I think it has a good chance of being effective at reducing overall gun violence rather than (or preferably in addition to) laws which specifically target weapons typically used in mass shootings which are a very small portion of total gun violence deaths (despite their horrific nature). They also need to increase the budget, manpower, and research capabilities of the ATF which have been limited by special interests and some in Congress.
Chicago and other cities can have strict gun bans within their city limits all they want, but it won't be effective as long as anyone can just drive outside the city limits and illegally purchase a gun from a legal (but corrupt) firearms dealer or relative any time they want.