Yes they do. Becoming CEO of a company like Disney is just as political as becoming President.
> They can, and do, purge their ranks of dissidents.
So do Presidents. Every 4 (or 8) years a new President is elected and they replace the entire cabinet. This is probably more disruptive than a new CEO coming in and replacing a handful of disliked executives.
I don't think being a Fortune 50 CEO is necessarily the best preparation for president, but there is definitely a lot of overlapping skills. This is very different than the businessman as politician fetish the country often has; running a small/family business doesn't require the same skillset.
Of course the President can fire the people who disagree with him. In fact he should do that if the people are preventing the implementation of the President's lawful policies. The Constitution is pretty darn clear on this point:
Article 2. Section 1: The executive Power shall be vested in a President of the United States of America.
Of course it is also possible for a President to make poor decisions, but the trend towards criminalizing policy differences is not a healthy one. Elections are the solution to poor executive decisions, which is NOT the same thing as unlawful actions.
CEO's don't have to build consensus. They can, and do, purge their ranks of dissidents. Iger, in particular, has been aggressive about this over time.
You cannot simply "fire" the people who disagree with you when you are President. We have seen what happens when you try to do that.