There is nothing untactful, or insensitive, about a stillbirth being named as a stillbirth. The baby did not die young, as that implies they breathed after birth so to die. They died before they were born.
Such a category is factual, and the new sticker for such babes, came about after much lobbying from people who had lost their unborn to stillbirth.
As someone with multiple miscarriages and stillbirths in my family (some to close relatives, some to not so close), I cannot see why it would be considered insensitive to use the term that is correct.
Should we also ignore that a "miscarriage", as we now call it, was also historically known as "spontaneous abortion", just because the word "abortion" has come to mean something else? As family historians and researchers it is our (often sad) task to name things as they were.