That’s a good analogy, but I think the reason we currently need the "nurse" role is the need to interact with the physical world. Most software products don't require this step, so the demand for “nurses” or "doctors" will likely decrease. If robotics technology continues to advance, the number of nurses in real world will also decrease in the foreseeable future.
The demand for nurses and doctors is only going to go up. Not just int their current roles, but everything adjacent to them as well. Everything involved with running trials of health care products. Humans aren't going away, and they need to be taken care of.
Nurses will likely be one of the last professions to be significantly impacted by robotics. Drivers, factory, warehouse, agriculture workers, cashiers etc will be automated away way before them.
It's just hard to design robots that can handle patients that may be simultaneously fragile, mentally handicapped and aggressive in a way that doesn't hurt them and respects their rights. It can take multiple human nurses to do a seemingly simple thing like changing a diaper.