Right, so the word "purpose" has more than one meaning or use. The way Trevor and Viv use it below is in the personified sense, usually suggesting that the universe or god or evolution has some human-like thinking process, which they both point out is non-sensical and I agree.
That's not the sense I used the word though - I meant it in reference to an inanimate object, in this case government and specifically an impersonal leviathan government, not the local HOA. In that sense, most man-made objects do have a purpose, assuming the creator is man and the individuals involved had some goal or purpose in mind when creating the object.
A rock in a field somewhere has no purpose and a human life in the context of the universe has no purpose greater than a bacteria on the back of a moist rocky moth circling the big candle in the sky... but a fork has a purpose - to move the peas from your plate to your mouth in a more civilized way that scooping them up with your fingers.
As Trevor points out, purpose is not inherent in the object, but depends on goals, desires, need, etc. at a specific point in time, so that the fork could also have the purpose of opening a can of paint or occupying a place of honour in a wall decoration or for stabbing the shoulder of your friend who just wouldn't shut up while you're trying to take a nap.
Government is a man-made object which requires and demands substantial upkeep and does not conveniently confine itself to the cutlery drawer until needed. It imposes itself on our lives daily and in countless significant ways. So it is interesting to know why - for what purpose and to what end ?
I have been searching for that answer for about 4 decades now and the only reasonable answer I have gotten in all this time is from Pinker i.e. government as an omni-present and omnipotent substitute for god makes us refrain from stabbing our buddies with forks. It makes people think twice about hurting each other, which has lead to the world being a more peaceful place than it has ever been.
The rest of what it does still seems evil, nefarious, bogus, wasteful and unnecessary, so in an ideal world I guess we would want to have a foundation of peace and leave everything else to individuals. I'm still new to this conclusion, so I don't know exactly what that would look like or how one would contain it to that single purpose, but now I'm starting to get how Leon and others could support the rule of law, which did not make sense to me until now.