If the government can’t possibly do anything resembling justice, then what IS it supposed to be doing?  If people think we should have a government at all, then I would expect them to feel a need for that government to settle issues in ways that they consider reasonable/satisfying (mostly, on average, etc), or else what is the point?    

Different things are getting combined here, through legerdemain.  Or, at least, that is how it seems to me.

There are obviously lots of very helpful things that the government can be doing. 

Even just limiting ourselves to the very narrow arena of law enforcement:

I expect the government to protect me from crime, to the fullest extent that it can do so (without putting intolerable strain on other values, something something civil liberties).  In the name of doing this, I expect the government to provide reasonable levels of deterrence to would-be criminals.  If in fact I am victimized, I expect the government to provide me with fair material restitution for my loss.  If I come under suspicion, I expect the government to provide me with expeditious due process of law.  Etc. etc. 

I do not expect the government to make me feel better about the situation, or to give me “closure,” or to reflect any sacred abstract principle.  All those things seem well outside its powers.

…I suppose, if you want to play nit-picky games, you can ask “don’t you at least expect the actual criminal codes of the government to be just and to reflect justice?”  And the answer there is…no, I don’t, not really.  Justice would smile upon first-degree murder in certain cases, and would make rude words a hanging offense in others, based on circumstantial details to which no government could possibly have access.  Justice would require a sublimity of understanding, and a grasp of nuance, that isn’t even theoretically achievable at the level of a large-scale institution.  As a practical matter, I expect the government to agree with my sense of justice in a very broad-brush sense on certain important matters (like “murder and theft are usually bad”), because as a practical matter most humans tend to think the same way about a lot of things, but that serendipity ends well before the point where I would entrust the state with my psychological or spiritual satisfaction.