Why is politics, which should be a profession conducted in service of the people, carried out so badly?

Because "Every nation gets the government it deserves".

It's not carried out badly in most countries.

In those that it is carried out badly, various forms of corruption are obvious. For example in Japan, there is the corruption that government workers are not really expected to produce results. In the US, there is the lie being spread by the right wing that government is incapable of functioning (look to this very page for an example of that lie in action) in order to trick people into allowing the government to prey off of them.

But there is a good deal larger of a world than just the US and Japan.

Trump used to say things like that. Now he's quieter on the issue, after finding out that running a government is a million times more complex and difficult than running a corporation.

The problem in most democratic systems is that it takes money to get elected, and to get money, politicians need to sell themselves in service to their donors. They may start out wanting to work for the people, but the system is structured in such a way that by the time they get to a position of power, they no longer have the leeway to place the needs of the people over the needs of their donors.

which should be a profession conducted in service of the people

The problem is that assumption.

JeffLee’s point is a good one. I used to dislike the idea of career politicians but now I’m not convinced that bringing in an outsider works either. People from outside politics can be naive about, or utterly ignorant of, how government works and how difficult it is to get things done. I read a persuasive argument that rather than shaking up the system, naive outsiders rely more on those most interested in keeping the system in place.

When the politicians forget they serve the people and not the other way round.

Ther answer is simple: politicians are scum, but the world needs statesman.

People whose power is unchecked will always take the piss.

Unbridled greed. In my country, corruption is rampant everywhere in government.