A Question of Power
You get a monarchy or aristocracy when the country gets too big to be ruled by a less formal assembly of tribal leaders and elders, and when the commoners are not yet in a position to demand political rights for themselves.
I do not think that the FTL monopoly alone will be enough even if it can be defended; the planetary populations could demand home rule no matter who controls FTL. But more likely anti-trust regulators will step in to prevent a monopoly unless the would-be king already has power to make it stick.
North Korea: Three Generations of Dear Leaders
Kim Il Sung came to power as a Communist guerilla who fought the Japanese occupiers. His personal power and cult of personality have allowed his heirs to rule the nation without having fought in the guerilla war themselves. How did they do it?
- A society which respects ancestors and believes that merit can be inherited.
- A group of people who benefit from the status quo and support it. This is larger than the immediate Kim family.
- A larger group who are taught to be afraid of change because the night is dark and full of terror. The last time without the Kims was when the UN offensive got almost to the Yalu. Before that, Japanese occupation. Better the devil you know ...
United States: Two Generations of Bushes
The United States is totally unlike North Korea, yet they managed to elect two members of the Bush family within a few years. Other family members are in senior positions as well. On the other side of the aisle, the wife of President Clinton became a candidate for President herself. Why?
- An early introduction to nuts-and-bolts politics. A junior member of the Bush, Clinton, or Kennedy families will be more aware of how one runs for office and builds a political career than the average kid.
- A head-start in the race for public attention. If a John Doe declares that he wants to run for president, that probably won't be a headline. If a Bush does, different ballgame. Attention feeds upon itself.
- An inherited network of political contacts. If the junior has roughly the same political positions of the senior, the senior is tailor-made to provide personal introductions.
- Funding for the early stages of the campaign, before donations roll in.
You talk about a king and nobles. But that's just names, what you need is the power of a king or a noble. So imagine there is the Jump Gate Corporation. A large block of shares is held by one family, with some legal construction to make sure that it cannot be split. (A trust managing the portfolio?)
- There are many other shareholders. Some big (think a duke who is a near-peer of the king) and some small (a back country baronet, not terribly important but still due his courtesies). These people would be upset if the company was attacked.
- Through suitable education/propaganda, the non-stockholding commoners are taught that respecting property rights is important. After all, if the government could come and take Mr King's stocks away, they could come to the little guys and take their meager belongings as well.
- Startup companies bid for the right to explore new jump gate connections.
- When one does really well, it is purchased by Jump Gate Corporation in a deal that gives the startup funders a few shares in Jump Gate Corporation.
- In theory, everybody can found a startup. In practice, one has to know how to write a business plan, find initial investors, apply for the jump gate contract, etc. There are snake oil salesmen who promote expensive courses at Jump Gate University (not legally affilated with Jump Gate Corporation), but the best way to learn is to be born or married into a family who has done it before.