a place where patriarchy has completely collapsed, say present day Detroit
How did patriarchy collapse in Detroit, exactly? This is a city looted to the ground by corrupt bureaucrats run amok, a failed-state kind of phenomenon. I don't see gender politics playing any major role here.
I don't think that's what happened in Detroit either.
Really, what happened was that most of the auto jobs left, and much of the population with it. It's a city that's had a shrinking population for 4 decades now. That means a huge amount of abandoned houses, whole city blocks with only one or two people living on them. Because of that, you have a dramatically reduced tax revenue that's no longer able to cover the costs of adequate services, and you have all the social problems of abandoned housing (increased crime and fire risk) without the resources...
Speculation is important for forecasting; it's also fun. Speculation is usually conveyed in two forms: in the form of an argument, or encapsulated in fiction; each has their advantages, but both tend to be time-consuming. Presenting speculation in the form of an argument involves researching relevant background and formulating logical arguments. Presenting speculation in the form of fiction requires world-building and storytelling skills, but it can quickly give the reader an impression of the "big picture" implications of the speculation; this can be more effective at establishing the "emotional plausibility" of the speculation.
I suggest a storytelling medium which can combine attributes of both arguments and fiction, but requires less work than either. That is the "wikipedia article from the future." Fiction written by inexperienced sci-fi writers tends to generate into a speculative encyclopedia anyways--why not just admit that you want to write an encyclopedia in the first place? Post your "Wikipedia articles from the future" below.