I'm currently driving a Golf GTI 16V so it's not a cheap car to insure but points didn't matter.
But your right different insurance companies do look at things differently. Some like to know what you do for a living whereas my bike insurer never asked. Some want a 5 year clear driving record some say 3 years before you don't have to mention stuff. It all depends. I spend hours finding different quotes when it's time for renewal cos of this, after all nothing else to do at work.