Any time you build an industrial complex, you’re creating a new point for the Axis to attack, while slowing infrastructure development. So the question is not really whether a Brazil IC would be useful or not. It’s a question of how 15 IPCs are best spent.
If going Kill Germany First:
US1 you want to build a defensive fleet to escort transports to hit Algeria on US2. There’s no point in going to Algeria unless you bring some transports and ground units, so you want those too. The more transports and ground units you bring, the harder you will be to dislodge. Also, the more transports you bring, the earlier you can threaten Western Europe. Threatening Western Europe in a combination attack with UK means Germany will either have to pull units back from the Russian front (giving Russia more IPCs to work with), or abandon Western Europe. Either are fine. Once Western Europe is abandoned as a base for fighters and particularly bombers, the Allied fleets have far more freedom of movement, particularly for southwestern Africa and between East Canada and London.
If going Kill Japan First:
Alternatively, you want to race Japan’s two battleships, two carriers, 5-6 fighters, and bomber.
But in any event, if you’re using 15 IPC for an IC, you’re not helping your fleet infrastructure, whether Atlantic or Pacific. What you ARE doing is diverting attention away from what should be the focus of your attack, whether that be Africa, Europe, or the Pacific islands. Industrial complexes don’t fight. They don’t help shuttle ground units effectively, especially when they’re on an isolated territory like Brazil.
There’s things the Allies can do differently, like a sacrificial US transport to Algeria on US1 to start pressuring Germany immediately. But that’s neither here nor there - the idea is the same; 15 IPC spent on an industrial complex is not a good idea, at least until the Allies are dominating the game so much that it hardly matters any more.
Verdict: US industrial complex in Brazil: Not good. Unless you’re an athletic footwear company.
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This is NOT the same as Japanese industrial complexes on the Asian mainland. The difference is that Asian mainland ICs allow the Japs to build pure tanks. Initially, Japan needs to focus on infantry production with very light tank coverage for blitzing. But depending on German progress, the focus will need to switch to tanks at some point, and at that point 14 IPC of transports gets only two tanks to the mainland, while a 15 IPC industrial complex gets three tanks. Furthermore, industrial complexes give a great effective boost to mobility, as supposing Japanese tanks are produced at Tokyo on one turn, the next turn they can only hit points on the Asian cost. In contrast, Japanese tanks produced on the Asian mainland can usually hit one or more of Caucasus, India, Sinkiang, China, and/or Yakut.