I am not modern enough to follow “daas Torah” (if I am wrong, please give me a reference to the Gemora tha discusses daas Torah, I would appreciate it), but here is a couple of examples what we would ask Gadol for – a longer view.
1) Haredi politicians asked Menahem Begin to increase government funding for schools. Begin said – this is enough not enough, I’ll give you as much as other schools. Rav Shach told them to refuse and go to previous levels. Otherwise, schools will now rely on government and next government will change the rules
2) WW2, 1940, Vilno, question to R Grozdinski: should we use Sugihara’s visas for old Rabbis (Soviets will arrest them first) or young ones (whose children will be taken away to communist schools). His answer: old ones, they will be able to help remaining ones when they come to US, and also they wil be more of use to American Jews