The main advantage of having the staffing function centralized rather than dispersed is that it allows for continuity and consistency. It makes it much more likely that a single vision and a single set of policies will be carried out in all staffing decisions. It would be much more difficult to accomplish this if the staffing function were dispersed.
There are at least two main reasons why this would be beneficial. First, having centralized staffing means that all hiring will be done according to a central plan. The staffing functions will all follow a centralized vision for what the firm is trying to accomplish and what sort of workers it is trying to hire and promote. A second factor is more legal in nature. When staffing is centralized, a single set of rules and policies can be followed. This makes it less likely that legal complications will arise. There will be no chance for managers to make decisions that might, for example, be in some way illegal. The staffing function will be carried out by people who know the legal requirements and are certain to follow them.
For these main reasons, it is typically better to centralize the staffing function in a large firm.