A world government is something I wanted when I have still been naive too, but seriously, look at how society works. Usually smaller societies work far better than bigger. A world government is stupid, because even if thinks look like they would be more efficient they are not. The opposite is true. We actually should split things.
I know that's exactly the opposite of what most of us always thought to be the truth, but simply look at sizes of countries and then tell me that bigger countries are doing better. Simply not true. Big organizations have big problems.
Also, you are making a mistake if you think that there is something like a good politician or a good government. The thing is not only that you can't measure it in first place, but also that even if there is a politician where most of us could agree on to be good or at least not too bad it really depends on time and society. The best democrat may be the worst thing for the world tomorrow or would have been a few hundred years ago, maybe would even have prevented democracy from coming to existence.
Its also a bad option in an evolutionary sense. More small, individual, independent countries mean more experiments on government technology or in a biological sense a bigger gene pool.
Also it is the extreme form of centralization and I think most of us can agree that that's bad.
Also, if you have to care about the whole world you will act way too abstract which of course is really bad in a lot of ways.
A better alternative would be the emancipation of people weakening the need for a government, so it at least has less to do. See
Small Is Beautiful. Also have a look at Leopold Kohr's practical work, really effecting societies in a positive way. He too wrote a book, called The Breakdown of Nations.
Or just see negative examples, like the US, China or Russia. They are all big in different ways. Then compare them to stuff, like Luxemburg, Switzerland, Austria, etc.
Also, to solve global problems you usually need something else than an (active) politician. You need people that actually do stuff. There aren't many (active) politicians that actually changed the world to a better. Doesn't mean they are not good, but it's a fact. There are lots of other people who did and a lot of politicians do more good stuff afterwards, when they are more free. Yep, that's maybe it. People work better on making the world better, when they are not bound to anything, be it the world of politic, time, money or whatever.