The Federation makes decisions that affect the state of the Galaxy, and they make different decisions than they would under Vulcan control

Eh, questionable. I'm sure many of us have been in situations where we're advising more senior staff and the manager or whoever isn't really the one making the decision anymore - they're just the talking head we get to rubber stamp what those of us who actually deal with the problem have decided is going to happen.

In practice I tend to find that the people who control access to information, rather than the people who wield formal authority, tend to have the most power in an organisation.