Why do some women get chest tattoos instead of insert after mastectomy?

Personal choice. Women have options after mastectomy: immediate reconstruction, delayed reconstruction or no reconstruction. Ideally all women should be given these options depending on the circumstance. Those who choose not to do reconstruction are making a personal choice. The great thing about breast cancer is that there are many options available. The earlier you are detected, the more choices you have.
Both! Most women who have a breast operation that sacrifices the nipple not only get reconstruction of some kind, but they also get a fake nipple made. This involves a minor skin operation, which raises up a nipple-like bump, and a tattoo.