- It's direct point to point communication (over a network)

- The transport network is dedicated and not open to anyone and covered by quite strong laws in many countries

- It's easy to see the history of communications

- It's easy to see if the other end successfully received something

- It's relatively standardized and ubiquitous ( in health )

Email would be the closest thing, but it doesn't have all the advantages, and the extra add ons that would make it better (like encryption, delivery receipt, digital signatures) are not standardized and/or ubiquitous ( and often hotly argued about )

So fax is the lowest common denominator, that, if it was proposed today, would not be accepted for many of its disadvantages, but it's now hard to find a way to replace it.