Dermatosis papulosa nigra, also known as DPNs, is a common condition, especially in people of color. The condition usually runs in families and the lesions are easy to remove using a hyfrecator or a scissors. Costs will vary. Some people charge by the lesion e.g. $25/lesion or by the batch e.g. $300 for 10. As cosmetic procedures go, DPN removal is generally affordable and in my experience, very satisfying for the patient. One does not have to remove every lesion to see a major difference. Make sure this procedure is done by licensed health professional. I don't believe it is legal for aestheticians to perform this procedure in many states.
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.