While the experiments were obviously extremely unethical (among many other things), did they have any profound effect on modern healthcare?
Not at all. Apart from "extremely unethical", as you say, the experiments carried out by the Nazis were also extremely unscientific. They were more an excuse for cruelty and an attempt to "prove" racist ideology than an attempt at medical inquiry. They yielded nothing of value. You can read about this in more detail in this older answer by the stalwart /u/commiespaceinvader.