Isn't it true that strong vision that people have a true emotional response to and believe in can move 100k people (or even more)?
Maybe an expensive "true rebrand" is a way to make a promise to your people and help build trust in your new direction. Also making it so visible and present can help remind people of this direction when they make every day decisions.
The problem is not only the number, it's the overall inertia between what management wants and what workers are all levels can get to. Management may have a forward moving vision, but it takes time to communicate it, to ensure everyone understands what it means, etc... and there are always resistances, too.
Plus, in a 100k company, I don't think 100% of employees are blindly following what the CEO wants them to do.
Maybe an expensive "true rebrand" is a way to make a promise to your people and help build trust in your new direction. Also making it so visible and present can help remind people of this direction when they make every day decisions.