Lots of questions, but I'll try to answer:
Forming without a Ruling Body
A completely urbanized planet might be able to form without one ruling body. This would mean that the different countries on the planet would have to be very trusting of each other. Or at a point in war where you couldn't destroy each other's cities.
In the Middle Ages, France and England were at war. Along one river in France, each country would build a castle, each on their own side of the river. Around these castles towns would form, the two enemy towns may be very near each, even though they were at war. Cities on an urbanized planet could form similarly. Even if both countries were at war, the cities could come up to the boundary line (or very close) if the technology or incentive was there not to attack. In the case of France and England, the river prevented a quick attack on the opposing town, meaning that the town would have time to flee to the castle and be protected.
If the two countries were allies, then they might not object to building cities right up against each other. There would probably be a small boundary line, but this would be negligible to the size of the city. It might even be used as a park.
Why Such a Planet is Good
Cities provide great opportunities. 878
They are the sources of jobs, because the jobs can find labor. They are the source of government, because the governors need a place to meet. If cities kept growing, with bigger corporations and bigger amounts of work, it could be economically beneficial. It might also be more efficient (more people in a smaller space), keeping scientists together so research could go on. It could also be politically useful, everyone in one place is easier to manage than having them scattered across the stars.
These are all reasons to do this if you had the ability to travel to other habital planets. If you couldn't travel, a planet-wide city would merely provide you with enough space to house all your people.
I don't see why there couldn't still be private landowners, it is just likely that a land owner would get a "cubic" plot, meaning that their land doesn't necessarily go up into the sky forever. This would make it easier to build large sky scrapers.
Summary
Your final section of the question asks why this could happen. I believe I have already answered that, but I will summarize.
Such a planet might exist if there were a single government and the population needed a planet-wide city to provide enough space. Or it could exist if the government thought a large city to be economically or politically beneficial.
Such a planet might exist if there were multiple governments and they were at peace. Each government would extend its city as far as possible, for the reasons above. Or if the planets were at war, a system were each side couldn't attack the other would allow for the reasons above to take over. 121