This is a relatively common condition principally in darker-skinned people. It consists of multiple, small pigmented papules on the face and neck. It tends to run in families. Bill Cosby would be a good example of this condition, as would Morgan Freeman.
Treatment is for cosmetic concerns only and consists of shaving the lesions off (if they are larger) or using light electrocauterization. This is why your insurance won't pay to have them removed. The sites are benign, so insurance considers removal cosmetic, and will not pay. Initially, only a few should be removed to be sure there is no hypo or hyperpigmentation afterwards
If you'd like to have them removed you could see a dermatologist or dermatologic surgeon and discuss pricing options, especially since you will need several procedures.