Hopeless War: Averted, for the most part. With regard to one kind of hopeless war, well, the Navy and Legions are just that good at the general category of activities listed under “killing people and breaking things”, and so have usually been able to bring things to a successful conclusion (and the kind of ruthlessness that tells them when to back off and bring out the really big guns, as in, say, the Burning of Litash, also helps). And even the ongoing stalemate that is the containment of the Leviathan Consciousness has settled into a status quo that isn’t chalking up casualties in huge numbers any more. It’s still theoretically possible, it just hasn’t happened yet, and there are lots of smart people trying to make sure it doesn’t.
Averted in another way (although subverted, I suppose, in an early sense with the Consolidation Wars) because despite the Empire’s earnest desire for ideological propagation (see: Hegemonic Empire), both the Ministry of State and Outlands and the Admiralty are appropriately cynical about the possibility of wishing civilization into existence when people aren’t willing to cooperate, of persuading the former oppressed that oppression isn’t great fun when they get on top, or for savages to spontaneously start behaving nicely, and other such things, and thus are far too situationally aware to get bogged down in something like an Afghanistan, or an Iraq, or a Somalia, or other types of “nation-building” war where the hopelessness comes from setting yourself a comically improbable termination condition.
(And where one of these more… regressive members of the Interstellar League of Tribal Chiefdoms starts to play host to terrorists, or some other thing that actually makes them a threat, however trivial, to one or more of the real players… well, then, it’s time to bring out the time-honored “Shell Them Back Into The Stone Age With Ortillery” strategy, which can be repeated half-a-dozen times a century for a much smaller budget than a single occupation would require. In the limiting case, see also Genocide Dilemma.)
Of course, some would argue that the overarching strategy of “Leave Them Mostly Alone, to Grow Up or Die Out” is itself pretty damn hopeless. Which it is, its proponents agree, but at least it’s the kind of hopeless which doesn’t get a whole pile of people killed, even temporarily, in the course of proving it.