I think part of the reason you are struggling with this is that you need to unpack your question before you can answer it.
The main function that Socrates claims is that of a gadfly, one who tries to make people aware of their own ignorance and challenge lazy, conventional modes of thinking. He does this by having conversations with small groups of people, including those who claim to be experts, and showing that self-proclaimed experts don't know what they claim to know.
This is a purely individual task, not something a government can do as a government. If we think that having people around who act in a Socratic fashion is valuable, we can use our power as voters to elect representatives who vote to fund such activities or we can donate money to support such activities. For example, we can support the National Endowment for the Humanities and various private foundations that provide grants to writers, scholars, and artists. We can support PBS and other forms of publicly-funded and crowd-funded journalism.
As for democracy, Socrates opposed it, considering that it was a system that appointed people simply because they were popular (or because they were chosen by lot, as was the case for certain positions in Athens), but not because of expertise. Question time (Britain) or question periods (Canada) in which MPs can put questions to a Prime Minister are somewhat closer to Socratic questioning than the U.S. Presidential press conferences, but neither really resembles the form of extended dialogue with a single interlocutor that is essential to Socratic elenchus.
The system of long adversarial speeches in the Supreme Court is something Socrates would not approve of, as one can see in his criticism of rhetoricians in Gorgias, Sophist, Apology, and Phaedrus. Cross-examination would be slightly better, but still, it isn't really a cooperative quest for truth.
As for helping other countries, this really has nothing to do with Socrates, who evinced no interest at all in "barbarians" (the Greek term for those who did not speak Greek).
A more productive area for you to discuss would be our educational system, as Socrates was very interested in educational reform, something discussed in many of Plato's dialogues. Socrates was also interested in how people should raise children and how the ideal state might function. Those would be three areas that you could discuss on the basis of dialogues by Plato and Xenophon in which Socrates appears as a major character.