Government is far from the only thing that maintains "order". I sincerely doubt that the 'fear of getting arrested' is the only thing that keeps me from murdering people on the street, for example.

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.

I agree government should be constrained. That said, while government may not be the only thing keeping you from murdering people, other reasons are not shared across the whole of society. We don't all organize around your religion or moral code, let's say, and because of that, we have government.

It's true that government as a group of representatives of all people is slightly different from the now self-aware monster the (U.S., insert-your-personally-experienced-representative-government-here) government has become. But it's still the single organization we all agree to work through, and so changes made across an entire society most likely have to go through that government.