At least two destroyers are needed to run each support expedition (normal nodes and boss node) for world 5+ and event maps. And there have been some event maps that require your fleet to be mainly composed of destroyers (eg. Winter 2015 E-1 map). So if you ever encounter such a map and want to use support expeditions, it is a good idea to have some spare DDs ready.
Aside from event maps, there is map 3-2 that allows only all DD fleets to reach the boss node. So it's good to level up some extra DDs if only to pass this map.
Lastly, the main attraction of leveling up Fubuki is for her Type 94 Anti-Aircraft Fire Director, which can be upgraded into a 10cm Twin High-angle Mount + Anti-Aircraft Fire Director via Akashi's arsenal. This allows for AACI (Anti-Air Cut In) which will make your life a hell of a lot easier when fighting enemy carriers (assuming it procs).