Andrey,
In developing countries (usually) the economics of healthcare is too many patients and too few doctors. Doctors see about 50 patients a day. In such a context, the information gathering phase of a diagnosis tends to collect fewer data points as time is a primary constraint. Doctors could lean on mental heuristics such as the availability bias, overconfidence etc to perform in such short turnaround times. We can use BOTs to collect additional data points that would have normally been missed, increasing the number of data points per consultation.
This was the idea behind our Chatbot. We faced challenges such as what personality she should have. If we gave her a very human name, patients obviously did not want to share information. If we gave her a very robotic name, patients were fine sharing information with her.
To answer your main question yes of course! Bots can be used for better healthcare.
More power to them!
Akshay