First up, what does competence mean?

Competence means both the understanding of how to do things + the ability to get them done. For example, I am absolutely incompetent at boxing. For the clear reason that I have no expert knowledge of how to fight with my hands. How best does one make a fist, so as avoid breaking one's own fingers as they land their punches? Or move, to enable ease in evading punches thrown by one's opponent and quickly surging forward to land hopefully successful ones in return ... all without losing one's balance? I have no idea what answers to these questions are. And that's only the understanding part of the equation. Whether I have the right physical traits or mental strength (ability) to enable my boxing is a whole different matter.

Clearly, competence is a difficult thing to achieve, and most people are incompetent at most things. The same thing interestingly is true of governments. Most governments are incompetent at their job. What is that job and why do governments exist at all?

Why governments exist

Some people, referred to as anarchists (there are different factions of them, an especially popular group are called "anarcho-capitalists") are convinced that governments (central coordinating organizations) shouldn't exist at all.

The specific beliefs of different anarchist groups have slight differences in them. The fundamental belief common to them is the idea that central organizing bodies (central governments) — which have a right to compel people within their territory into doing their bidding — shouldn't exist. The systems each faction proposes to replace that defer in lots of different ways.

Why do anarchists oppose the authority of central governments to compel people in their territory and seek to abolish it? They believe that governments impede a default right to freedom of humans. Think about it. The moment you are born in a country, with absolutely no consent of yours to the laws of that country, you immediately come under those laws anyway. Why do you suddenly have to pay tax to a government you didn't choose to govern you? Why does the police (agents of the government) care about what you do? Why wouldn't they just mind their business and leave you alone?

(most people in reality have never wondered about these questions. Since no one else/not many other people... is/are complaining, they do not complain either. This is why it is good like we earlier referred to in the discussion about how one might seek to reform a flailing African country that people are sheep. It makes it easier to align human goals. Most of the people who do question this phenomenon are sheep too, they do it not because they independently came up with the question, but because they think it's cool to ask such questions).

You might even imagine that you could win a legal case against a government in court in the fight against taxation. After all, no where have you ever consented to being a citizen who gets to be docked a certain percentage of your income. For what? When your birth certificate which might be argued is implicit consent to the rules of the country was issued, you were underage and without the ability to give consent. It is all an imposition and flagrant abuse of power you could say. But is it?

Central governments are very powerful in truth. They usually are the most powerful entity in a geographical area. Having a monopoly of violence (ahead of dissidents, terrorists or criminal cabals) is one of the most important pointers to who actually governs a geographical area. But why do governments exist, and where do they get their authority?

How governments came to be

A long time ago, humans lived in small bands of hunter-gatherers, but more people working together means a better division of labor and efficiency — which is increasingly what happened, and is why we have large cities everywhere today.

Cities are capable of complex activities. There are enough people to specialize in lots of different activities. This is why large cities usually are the places where the more rare activities happen. It's about economies of scale. The more people there are to purchase a good/service, the lower the price can be, since the costs of production can be spread across more sales of the good/service. There is enough activity happening for even what would be unusual and rare in a small town to see some activity.

The problem with all of those people and all of that activity? Increased difficulty coordinating activity. Too many cooks spoil the broth. Someone/some people need to be in charge of coordinating activities of the very large community of people. That's historically why central governments have come to exist.

Recap: Human societies naturally grew larger and larger because of the advantages of scale, and there came the need to manage the interaction between people in those societies. And then there came to be rules and laws and agents of the government (police, courts) to execute them.

So while it may seem unfair that central governments seem to by default have a right to compel people to do whatever they want. They didn't come out of thin air. It's a time-tested system which slowly evolved over several generations of your ancestors. It's the only way things could work: with some people in the middle organizing how everything works.

The role of governments

We have mentioned the fundamental role of central governments above: to co-ordinate human activity. That is all. Everything governments do is downstream of that, including:

(i) security (protecting its people from internal/external danger) (ii) diplomacy (interaction with other governments in the interest of its people) (iii) construction of public infrastructure (to enable the activities of its people). etc

What is a competent government?

By our definition of competence above (both the understanding of how to do things + the ability to get them done), a competent government would then be a government which understands how to do its job and the ability to get it done. But governments are not people, unlike me with boxing. I can afford to be incompetent at lots of different activities. I couldn't possibly be competent at that many things even if I tried my hardest. I wasn't created with the intention that I be competent at all things after all.

Governments meanwhile were created with the explicit intention of absolute competence at a single thing: coordinating the activities of their people. This is why it is important to always remember the reason for their existence. It makes it a lot easier to evaluate their competence at their job.

Related:

— How might one reform a flailing sub-Saharan African country?