My understanding is that the anxiety isn't about a fear of programming being automated in the near future, but rather about ML growing into a required, essential skill for a software developer in the next few years.
Let's say you were an automobile assembly line worker in 1965, and you were hearing about robots taking over your job at some point. What would you do? That is, what would be the best thing you could do?
If you answer "Get an education in something that robots aren't doing, and try to get out of this career path" - go to the front of the line.
So - if you are a software developer - and worried that sometime in the future (I'd argue that "sometime" will soon mean "in 5 years, maybe less" - just as you note), ML is "rowing into a required, essential skill for a software developer" - what would you do?
Sit back, throw your hands up, and hope?
Or maybe get that education now on how ML works, how to use it, learning the hard math, etc?
Guess which route I have taken? Perhaps others should as well, if they want to continue in their careers...
Projects like TPOT and DataRobot are already showing a huge amount of promise for automating the tedious/time consuming parts of ML. But this doesn't mean they'll get good at the hard part any time soon.
I'd say your time/energy is better spent lobbying governments for socialist reform than learning ML at this point so we can avoid the worst case scenario(s).