Government is merely one component of society, (or "civil"-ization, if you want to be somewhat more colonial about your usage). Specifically, it's the axis of society where we condone the non-consensual use of physical harm (or threats thereof) for various purposes.

I guess what you are saying is that the list of purposes should be unconstrained ('whatever it takes to meaintain order'). My contention is that in general, an unconstrained mandate exacerbates social inequality because the agents of government will have self-reinforcing biases, and their unconstrained judgements can be weaseled into whatever justification they choose. Specifically to address your position, the pursuit of 'order' is ill-defined, and historically has led to very bad things like colonialism in the somewhat distant past, and things like racial profiling in more recent memory.

What constitutes 'order' is a very normative and subjective concept - for example, you might consider a group of young minorities hanging out on a stoop to be 'disorderly' and sic the police on them.