Is death by lethal injection "healthcare"? You can't escape the argument that abortion is doctor-assisted homicide by claiming it's healthcare. You can certainly argue that it's not homicide, because the thingy isn't a person, and so cannot, as the lawyers say, be the subject of homicide. But just because a doctor does it, or the pill causing it is approved by the FDA as safe and effective, doesn't make it "healthcare."
I am pro-choice, and I think states that ban abortion are wrong to do so. But specious arguments are own-goals, because they suggest those making them have nothing better to say. "Abortion is healthcare" is a politically counterproductive slogan. The sooner it is abandoned, the better.