I'd never heard of In Dark Alleys before, but it seems like it doesn't quite know what it wants to be. The break down of the psyche is so individually detailed but overall broad it would be a useful tool for any character creation. Quantifying the elements of a character like this helps give an idea of who the character is far better than any alignment or snippet of backstory. Mechanically I love that your nature can backfire on you, so long as whoever is running the game doesn't use it to take too much control away from players.
The biggest question I'd have is why go super natural? It seems like such a good system to throw curve balls at players in any genre of game. Espionage, fantasy, sci-fi, even something that is grounded in everyday life could be made into thought provoking commentary by the author of a world using the systems in a way a short story or film couldn't. Maybe I'm missing some of the point since I haven't dove into the material but it almost seems tacked on to give the players some action and an over arching goal.
I suppose this highlights a part of table top gaming that draws me here. Anyone can write rules for a system and any one can change them for their own group. I'd have fun just making characters with the psychodynamic system. Rolling through situations on my own would still have twists that challenge me since the game almost gives cues. Even by myself I'm not writing a story alone. It's the kind of story telling that, once you establish characters, you can really pick up at anytime. Just a chatroom and a few friends is all you need to start having fun.
There's a reason I didn't go into the world lore. It's a weird collection of supernatural strangeness informed by the aesthetics of abandoned buildings, urban decay, and a survey course in philosophy. But it in no way serves the stated premise of being about the status quo power structure.
A good example is one of the sample adventures. The premise is that friend of the PCs has fallen into a coma with no known medical cause. The PCs then receive a phone call from him. Turns out he's trapped in some other worldly plane that manifests as an abandoned city. After researching it's discovered that he was practicing lucid dreaming. While dreaming he kept coming across a black marble that seemed to want to suck him in. It eventually did. Now he's being stalked by some weird monsters and the PCs have to save him.
And that's it. It very much feels like it's "tacked on to give the players some action and an over arching goal." I find myself asking, "What does this have to do with maintaining the status quo for power?" Like it would be way more interesting to discover that beings at the hospital were mining his soul or something as metaphor for our broken medical system. Instead it's just "ooo a secret world and a monster."
It says a lot of your breakdown of the game that I could infer something like that. I don't see what's wrong with just making a system to get people thinking. You can help guide what kind of story is made with things like the skills and attributes you fill in when making a character. Obviously don't be ham fisted with it by putting in literal oppression points but something like the psyche can encourage players to think along the lines of less action more roleplay.