Frame challenge: Earth currently does have a single government over practically the entire planet just like your example alien planet does.
In our case: the difference is that the United Nations, which encompasses enough of the planet population that you could call it the planetary government, does not have the ability to do very much. But if we were to start relations with some ET planets and it was a transparent affair, then it probably would go through the UN.
In ET's case: the one-world government you suggest they have probably does also have smaller sub-divisions. Whether they call them a "country" or not has little meaning. So even if they have a one world government, their local planetary structure would probably be similar in many ways. The primary difference might only be in how much authority the one-world government has over the smaller units.
Further frame challenge!
This also assumes that a planet is supposed to act as a unified whole and that a territorial hierarchy is followed easily. But lets look briefly at a few other cases.
A planet could have two competing top-level governments. This is actually another common theme in sci-fi stories, where the population of the two halves of a planet are unified separately into two half-planet governments which are generally at war in those stories.
What about when people start to colonize other planets? Do you expect Earth, Mars, Venus, Europa, and whatever else is colonized to each have their own planetary government, or maybe even one system-wide government? But what if there is 1 Earth government, 1 Mars government, and the people of Earth and Mars independently colonized Venus and Europa? Now Venus is split, but it cannot be fixed into a 1-world government because it is governed by two separate governments which are already 1-world governments independent of each other, and likewise for Europa.
What about when ET races mix? So let's say your ET planet somehow managed to get everyone to get on the same page, have the same preferences and agree on a government and set of rules. But now ETs from some other planet which are different from them start moving to their world because they have a loose immigration policy, but these other ETs have different values, drastically different. That ET planet might not be able to be a 1-world government after all.
What about when multiple ET races independently colonize the planet you just discovered? Similar to the previous case, but let's say the planet you just discovered was not the original home world of any single ET race to begin with. It has 15 different colonies on it, each from a different race of ETs. They are not likely to have a 1-world government, especially if each one of them is still governed by their home world.
Disengaging from frame challenge...
To get strictly back to what you were asking about for a moment, just think about any huge empire that fell in history. Rome is the obvious one. Later on England and Spain controlled huge portions of the planet during the colonial times. But historically governments which grow to control most of the known world eventually lose control because they are over-extended. There is your data, sort of.
You might be able to argue that this is no longer the case in the current age when we can talk face to face with people on opposite sides of the planet by video conferencing and when you can move yourself anywhere in the planet within a day or two or have armies or relief efforts in place in days or weeks.
So now we have the technical capability to manage planet-scale governance. But even now the growth of political hierarchies has been stunted because of the differences between people.
Case study 1: United States of America
In the United States of America, there is already much opposition at the state level to the federal government - and there is opposition at the city/county level to the state level in many places. There have been multiple threats and movements in the USA recently for states to secede from the US and by counties to secede from their states, because the higher level government is opposed to their values.
Many states actually did try to secede in the 1800's, hence the civil war. More recently, significant groups of people (but not significant enough to succeed) from multiple states have called for secession again, many of them in Texas and other southern states.
Several counties in Colorado tried a few years back to start a process to split Colorado into two states.
Lots of people express a similar desire in New York state since the democrats outnumber the republicans just enough to dominate the politics despite most of the democrat-supporting populace inhabiting a much smaller area in and around New York City.
Case study 2: European Union
The same thing is being seen in Europe. Brexit is the obvious example. But again, just like in the US, it runs even deeper: there is often talk at lower levels of government of leaving the country, such as the Scottish independence referendum which came close to succeeding last time.
So even now that we have the technical capability and some people have tried to take the government hierarchy to the next level again, we are seeing that the differences between people is causing those attempts to either stagnate or break back apart into local governments again.
To overcome this, you need to get everyone on the same page. That is something that millions, if not billions, of people try to do every year, so we have possibly Trillions of failed attempts to get groups of people to figure out some sort of compromise between their preferences. This is not a good track record.
The track record is further stained if you look at individual communications. Right here on StackExchange you can see people refuse to get along with those of differing opinion every day, and that is despite the fact that StackExchange is not a good medium for that. You see it worse if you go elsewhere.
I think the most likely way you could even attempt to make that work without breaking apart (I'm going off into proposing political theory now, so I'll try to make this brief) is to borrow an idea from the Romans and let different regions manage themselves. We started to have that mentality in the United States of America as the federal government was not supposed to be able to control the states, but that has not been the practice in recent generations.