Under what conditions do you think a company would hire someone as a figurehead instead of letting the person have real control?

In the condition of the United States of America, yes I mean the President, just a mascot for the masses.

If the person who is controlling the situation has a bad reputation.

Possibly if there was a powerful former leader as chairman of the board who still wanted to be the real power behind the throne.

A fake company for the specific purpose of money laundering.

Take a huge company with a terrible reputation like BP, and put someone very likable, like Billy Crystal, in charge. People hate BP, but they would suddenly think the company has significantly changed, even though all they have done is changed their figurehead.

If the person controlling does not like media or other attention. He can let the legal head to handle all those work and focus on the real job