One major advantage of centralizing staffing is specialization. Although unit managers may know the business of their units (e.g. manufacturing, web design, etc.) they are unlikely to be up to speed on human resource issues such as regulatory compliance, detecting fraudulent applications, attracting an ideal applicant pool, disability accommodation, managing diversity, etc.
Another issue is efficiency. If unit managers are being trained in and handling HR issues, that is time they are not devoting to their actual jobs of managing their units.
Optimal staff development may requiring grooming people for managerial or executive positions by moving them from unit to unit, something a unit manager would not be in a position to do.
Finally, in a large corporation, strategic HR goals might include rotating people through positions in several countries to forge a globalized corporate culture and filling high level positions through intra-company transfer when possible, issues that a unit manager is not placed to address.