What are insurance companies looking for, new and current drivers

Well I was almost faced with being without a job , thanks to the company I work for they don't treat us like a number and a warm body to fill a seat . They were in the process of switching insurance and again I had to explain a few not at fault accident In my class D. Actually 2 of the 3 were from drivers texting but anyways in Wisconsin all a NVR Report shows is.. accident dates and vehicle class . Even after explaining them they still refuses to insure me. Now most bigger companies wouldn't think twice to can a driver to save a few bucks . Someone sitting behind a desk gets to decide who is capable of doing this job . I know their is a few ways companies screen driver's. I've had a few minor warnings lately and even that would be enough to get a pink slip for most companies .