Minarchy? Not a good idea at all. After all, it is the policemen and soldiers who are the main, and is a certain way, the only true problem, not politicians. Politicians just say this and that. They have no power of their own. It is their pets who put "this and that" into action and practice. https://m.youtube.com/watch?v=ZSqBNGxLiAs
The problem with small government is that governments are like parasites. They grow, no matter how small. And they always grow at the expense of the public. America is the perfect example of this.
Look at America during the time of the Founding Fathers. It was arguably the freest country imaginable at the time. It stood for it's ideals: Life, Liberty and Pursuit of Happiness (although it took those from the Natives beforehand, and took those of sub-Saharran Africans afterwards).
Look at America today. It's a literal terrorist empire. First they violate your freedoms under the excuse of national security (Patriot act, increased police and military power, more surveillance, more airport security, attempted gun confiscations, war on drugs etc), then they violate other countries' freedoms under the excuse of them being 'terrorists' (numerous invasions, wars and bombing done overseas, gpvt overthrows and sabotages, oil and gold hoarding, military bases literally all over the world etc). There is a reason why US soldiers largely suffer from PTSD and have suicidal tendencies. Not because they witnessed atrocities. But because they commited them themselves. https://m.youtube.com/watch?v=4xsJXW4zKGA