The general rule for commas is that they represent a brief pause, for emphasis or an aside, when speaking. There's more to it than that. And this is one of those mores.
Without the commas the meaning is ambiguous. Besides its intended meaning, it could be read at least two other ways.
According to Sautter (1980), authorities feared that the end of the war would leave (thousands of workers from the weapons industries) and (at least half a million “demobilized” soldiers out of work and out on the streets). Read this way, "out of work and out on the streets" would apply only to the soldiers.
According to Sautter (1980), authorities feared that the end of the war would leave (thousands of workers from the weapons industries) and (at least half a million “demobilized” soldiers) (out of work) and (out on the streets). Read this way, "out of work" would apply only to the workers and "out on the streets" would apply only to the soldiers.
Out of context, and knowing the intent, the alternative constructions might seem unlikely. Also, we might all agree that in any context the alternative constructions would be considered poorly written. But it's not the job of the reader to figure out the most likely meaning or the reading that makes the writing seem better. It's the job of the author to make the text clear and unambiguous.
The commas also distinguish primary and secondary categories. The group within the commas, in this case the soldiers, is secondary to the group outside the commas, in this case the workers. That the primary group is thousands and the secondary group is half a million is unusual. But it's not unreasonable for the authorities to be more concerned with civilians than with military, even demobilized military. The reasons for this are beyond the scope of this question and I won't digress further.
The point is that the commas are necessary for all of these reasons. A long sentence requires pauses when spoken. There must not be any ambiguity. And the relative importance, if any, of identified groups must be clear.