So for the example of an actuary, ideally their job would also be automated by an advanced program. Not an impossibly advanced one, mind you - it certainly would not have to be smarter than even the 50th percentile of programs out there today. If we took every actuary working 9 to 5, and instead threw all of their tens of thousands of daily working hours at coding a program to do their job, how soon do you think we could automate an entire industry?
This extends to all jobs, eventually. You are seeing it happen today, with farming. Tomorrow, we will see taxi and Lyft drivers replaced with self driving cars, and mail/package delivery given entirely to robots and drones.
The moral of the story is we should automate jobs that people don't like doing.
I don't appreciate the fact that you run so far away with this doomsday scenario of "no insurance means we all get sick and die". Try to focus on the discussion the article wants us to have, not on the side-scenario that you want to use to rationalize actuaries or other poorly optimized vocations.