I would make an argument that any government can be stable. There are many, many options for each government type, and the government type is assigned based on what fits best. Therefore it does not always accurately represent what is going on in the world. (Spinward Marches, p. 124-125)
It's not common, but there are many real-world examples of how such a planet might develop:
0: Clans and families mobilize into efficient production units. You see this on a small scale in Amish and Hutterite communities. It would make sense on a planet that started out as a colony and gradually overtook the main planet in economic significance.
1: Company or corporation in charge of the full settlement of the planet. This is likely and unhappy situation and the citizens are exploited and cannot escape the planet due to being paid only in scrips usable at on-planet stores. Nevertheless, it is a stable if not ethical government, and the people running it are definitely wealthy.
2: Athens worked off of a participating democracy and was a trade and cultural powerhouse in the ancient world. This becomes even more likely as communications technology increases.
3: An ossified government that handles trade. Most of the lower caste have their own rules and laws, possibly being a lower tech level and/or using a barter rather than cash system. The lower caste is happy to let the government handle the administration of trade as long as they get paid. Such a government would likely track inflation and increase payment to the lower caste as soon as inflation reaches x%.
I'm skipping 4-9, as they're the easiest to see.
A: Rome under Julius Caesar, Egypt under Alexander the Great - leaders are likely to gain power after a significant victory. Whether this leads to economic success or a slow spiral downward depends entirely on the person in charge.
B: There are enough examples of successful hereditary kingships that it shouldn't be uncommon, but Elizabeth I is a good historical example.
C: France and America AFTER their respective bloody revolutions. While not truly an oligarchy, it is similar enough for the UWP code to apply. This would likely be a short period (10-50 years) until a more formal government was established (possibly from members of the oligarchy if they brought the planet into prosperity).
D: The power plays of the Roman Catholic Church in the Middle Ages once again mimic this. While not always successful, certain dioceses did gain enough power and prosperity to control local governments.
The government codes are general guidelines, and some of these are more likely than others, but they happen enough throughout history that I wouldn't find any of them unusual on a Rich World.
This is, of course, just my understanding. Does this help?
