The causation may have been inferred by others.
Those who have lived here for some time can probably work out the causes of the unemployment in the various locations as opposed to other locations where unemployment is not as severe. And before I go on let me say that nothing I write here will be a revelation.
The stereotypical view on unemployment in metro Adelaide is that it appears strongly in the northern suburbs and in the southern suburbs. Both regions, if I can use that word, contain areas of public housing which were built to accommodate migrant workers who arrived in Adelaide during the later Playford years when the state govt. was trying to shift the state's economy from its largely primary production base to a manufacturing base. You can't manufacture without skilled labour so mainly British immigrants with in-demand skills were settled in those areas.
The post-war economic boom in Australia begain to die out in the early 1970s with stagflation and the oil shock. At the same time countries in Asia were ramping up manufacturing and presenting a competitive threat to Australian manufacturing. The children of those migrants who arrived as sponsored migrants, that is they had jobs waiting for them, didn't have the advantage their parents had in terms of work, so what we saw was a gradual rise in unemployment in those areas. Cut to the chase, now we see trans-generational, structural unemployment in those areas.
The other parts of Adelaide metro were/are more diverse in terms of demographics and occupations so weren't subject to the sort of devastation that hit South Australian manufacturing.
Anyway that's my take on it.
British migrants arriving now who don't have jobs waiting for them are disadvantaged in comparison to sponsored migrants in the post-war years. On the other hand I think many, if not most, arriving today, have private capital, usually from savings and perhaps sale of property in the UK and may have the luxury of renting for a while before finding work and making a more permanent decision on where to live. I think a sub-text in this thread is the worth of having a desirable address when looking for work. I have no doubt that, depending on the occupation, your address is important. Adelaide is a very snobbish community, small-minded, parochial, suspicious of "outsiders" and worried that newcomers will "take our jobs".
If you're a skilled worker in manufacturing and you line up for a job then I would think that an employer doesn't care where you live, they are more interested in your fit in the job. But it may also be that white collar occupations have recruiters/interviewers who are sensitive to postcodes. I wouldn't be at all surprised.