It would require several breakthroughs in robotics and AI to automate a nurse's job. And then it would still be unlikely that this kind of automation is saving costs.

Why not - after the first automated robotic nurse it seems unlikely the second one will cost more than raising and educating a human nurse.

For a company the costs of raising and educating humans are only a fraction of their taxes, which they might mostly avoid anyway. The costs of employing a nurse (robotic or human) for a year are much more relevant. And there I am skeptical current robotics can hold a candle to (relative) cheap human labor.