Why is my subsidiary idle and not setting up new firms?
A subsidiary that never expands is almost always short of one of two things: cash, or instructions.
Check its cash
The subsidiary needs enough cash to expand. A conservative CEO will only start building once the company holds a large cash reserve, so a subsidiary that looks solvent to you may still look too thin to its CEO.
Check its expansion strategies
Make sure you have set the Expansion Strategies for the subsidiary’s CEO. Without them the CEO has nothing to act on.

Expansion Strategies are part of the subsidiary’s management policies. See Subsidiary Company’s Management Policies for the full set.