Within any organization, you can have 3 or 6 important people pushing in completely different strategic directions. And it can be clear to any unbiased observer that there's only one good, responsible choice, but within your org that gets met with essentially "but that's just your opinion, man".
So you call in a consulting firm and they deliver what most of the people already know. The consultants don't need to be rocket scientists.
But afterwards, nobody can say it's just your opinion any more. It's now expert analysis that you paid good $$$ for, and everybody who disagreed before now basically has to get on board.
So it's not even necessarily political "cover", but almost like a referee that brings enough credibility to settle otherwise intractable internal disputes.
Also, this lets the CEO appear unbiased to all the people who "lost". So they can get on board with the new policy but not feel like the CEO shot them down personally, which is bad for morale, can lead them to quit, etc. (Just because they believed in the wrong strategy doesn't mean they still can't be super-valuable in the future in executing the right strategy.)