It gives someone the political cover to make changes beyond their typical power that they knew were necessary.
Many large organizations are compartmentalized into divisions that act almost as independent sub-organizations. In these organizations, someone might have plenty of clout/budget/authority to bring in a consultant in their division, but not enough clout to convince a cross-divisional decision maker without some help.
For example: The President of MegaCorp North America thinks the Director of MegaCorp Widget Sales is whiny and asks for too many budget increases without a plan to the President's standard. Meanwhile, the reality is that everyone in MegaCorp Widget Sales knows they need this new piece of software. So, the Director of MegaCorp Widget Sales uses $100,000 of his existing budget to bring in some consultants to do a strategy plan for phase 1. Those consultants write up the same things that the Director and his employees have been asking for, but they put it in a shiny proposal with plenty of buzzwords. This satisfies the President sufficiently enough to award the budget increase for the phase 2 implementation project.
Super common scenario:
* The business thinks IT is too slow to implement, and doesn't understand business needs
* IT thinks the business changes priority too much and doesn't even understand their own business processes, and it's leading to technical debt because the demands of the business are half-baked
* So, the business brings in a consultant who says they will do everything they want, without any push-back, in half the time