Not really, if you think about it. Calling in mortal involvement is the equivalent of dropping a nuke as cannon says.
The council is made up a collection of people who are hundreds of years old. That means, you talking about people
with vast experience. Politics is the ugliest job ever, and becoming a world leader opens you up to some deep scrutiny, about the time they find out your Birth Certificate is faked and then discover a picture of you eating dinner with someone from the civil war you will quickly discover you have just opened a whole new can of worms.
Now that isn't to say the don't wield power in mortal society they just do it through economic means, and not so much political means.
Economics is still very powerful, just not as direct and a lot harder to pin down.