The only circumstance in which an insurance company will pay for tattoo removal is if you have a persistent allergic reaction to your tattoo which does not respond to normal, conventional treatment.
Allergic reactions to the metal salt used in tattoos are fairly common. Cobalt, chromium, cadmium and mercury all can lead to a reaction in allergic individuals. This is clinically in the form of bumps or nodules. Occasionally there is an generalized eczematous response. Treatment is injections of cortisone into these bumps, sometimes supplemented with oral steroids.
Mercury, in the form of red cinnabar, is the most likely to cause symptoms such as itching, swelling and nodules. Occasionally, and I have seen this happen, a tattoo which has been lying dormant for years, suddenly erupts in an severe allergic reaction. One tip here, if you have had this reaction to the red in a tattoo, avoid contact lens solution with Thimerosal or vaccines that contain this mercury based product.
Incidentally, the other colors that can cause these type of reactions are: Chrome: green....Cobalt: Blue....and Cadmium: Yellow.