But if you need the same amount of people to produce the same quantity of product (jut in different roles), then, by definition, your automation does not conserve time.
On the other hand, if your automation does decrease amount of time spent per unit of output, and you run it at full capacity, then where do all the extra units go? If you say "other people", then that would imply that there was some heretofore unsatisfied demand that the market couldn't satisfy due to a labor shortage.
Automation is a great way to solve the labor shortage problem, but it's not always present. And when it's not present, you're just adding more goods without adding new workers (or increasing wages for existing workers) to afford those goods - so you'll end up with an overproduction crisis.
Note, this is not an automation issue. This is a capitalism issue, because in capitalism, the only demand that matters is the one that lets you make a profit. People who may need what you make, but cannot pay above cost of production for it, don't matter. Automation tends to increase the size of that category.
The question is not how massive it is in absolute numbers, but how does it compare to the amount of jobs that are replaced by automation?
And you know the answer to that question. If all jobs so replaced would create an equivalent number of "programmers, developers and QA engineers", nobody would automate, because it would cost more than human laborers.