The point isn't just whether it leads to higher productivity the point is that it removes the need for certain industries almost completely.
Just think about the amount of areas that digitalization have completely removed. Those are jobs lost that aren't created somewhere else in the same phase as it's destroying them. And most of those jobs are being outsourced.
With regards to your cobol example I would like to see where you get that idea from. There is a huge demand of cobol programmers today because of all the old financial/banking systems which no one really dares touching. So that's an unlikely claim.
Things are done because they need doing, i.e. there is demand for them to be done, whether they are digital or analogue won't change that. Outsourcing is a better explanation of what's happening.
The demand for COBOL programmers proves my point. Computers didn't eliminate those jobs. They just transformed them. So where a company might have employed 100 accountants to do their accounting, now they employ 50 accountants and 50 programmers or 10 accountants and 90 programmers... Anyone who could do one job could probably pick up the other.
Outsourcing is just the step before automation. The US lost 4 million jobs to China between 98-2004 in the same period the Chinese lost 18 million jobs to the robots. This trend isn't stopping, instead it will only continue faster and faster.
The tings that digitalization kills are things like the camera, the walkman, the video-recorder, the video-camera, the post-processing machines, instruments, the studio musician and I could go on.
These aren't jobs that then are created somewhere else. In most of the cases where new industries or new areas are made they either require extremely highly specialized education or they are very hard for most people to make any money in. The app store being a good example.
Your Cobol example isn't proving anything at all and your claim was wrong to begin with. You claimed accountants just became cobol developers which is simply a false claim. And the reason why there is a need for cobol isn't because of a new demand but because of a dwindling availability of an existing demand which is also going down until a new technology makes that completely redundant.
The point isn't just whether it leads to higher productivity the point is that it removes the need for certain industries almost completely.
Just think about the amount of areas that digitalization have completely removed. Those are jobs lost that aren't created somewhere else in the same phase as it's destroying them. And most of those jobs are being outsourced.
With regards to your cobol example I would like to see where you get that idea from. There is a huge demand of cobol programmers today because of all the old financial/banking systems which no one really dares touching. So that's an unlikely claim.