You can understand the Ferengi Alliance better if you understand the role of the Grand Nagus in Ferengi Society.
The Grand Nagus, and the Ferengi Alliance, act as some kind of government for all Ferengi, providing unifying elements such as Ferengi ships. Think of the Grand Nagus and his empire as some kind of big corporation which sells licenses to other Ferengi so they, too, can benefit from the advantages this brings. In that regard, it is similar to a franchise, where you pay for being allowed to be part of a bigger corporation.
It took a long time to set it up (According to Nog in "DS9: Little Green Men", it took 10,000 years), but it works, mainly because the Alliance is built on a few structures and rules which ensure its survival:
- There are rules in place (Namely, the Rules of Acquisition and the Bills of Opportunities). If you don't follow them, you risk being cut off the Ferengi market (in other words, your business license will be revoked)
- The Ferengi Alliance generally stays neutral in politics, since this opens up the opportunity of profit from all sides of any conflict
- The Grand Nagus is typically very business savvy, and we have seen him providing good opportunities to other Ferengi (of course, always with the goal of furthering his own profit)
- There are some checks and balances in place between the Ferengi Commerce Authority (FCA) and the Nagus:
- The FCA has some power over the Nagus, it has the authority to remove a Grand Nagus from office under certain circumstances
- Inversely, the Nagus can overrule decisions done by the FCA
So the Grand Nagus is the commercial leader of Ferenginar, and at the same time the social and political leader. The regulations given by the Nagus usually become laws, and these laws are generally recognized by everyone as being necessary to increase everybody's (ability to make) profit.
We can see throughout DS9 how this extreme focus on market interests and nothing else impacts the society. For instance, women are historically not allowed to make profit (let alone wear clothes). Changing this would at first directly reduce the profit of all male Ferengi, and therefore, it was never really given more than a passing (shuddering) thought.
To me it's obvious that the Ferengi are supposed to be a comical exaggeration of the capitalism of the western world - if state leaders are thought to being bought by big corporations anyways, it kind of makes sense to make the Nagus a CEO of the society, with only trade in mind.