Why replacing Fisher would not guarantee a naval staff

Would Beresford have been more willing than Fisher to establish a proper naval staff?

No. Both are described as resistant, and existing staff functions within Naval Intelligence suffered from habits of secrecy ill suited to political coordination.

Beresford is judged no more willing than Fisher to accept a formal staff. The objection is connected with senior admirals' freedom to make decisions without sharing authority or explaining themselves to colleagues. Staff functions already existed within the Naval Intelligence Division, so the Royal Navy's problem was not a complete absence of staff work. Locating those functions in an intelligence organization encouraged secrecy and restricted information sharing. Those habits suited intelligence duties but were poorly matched to the political communication expected of a First Sea Lord's staff.