I mean, the most basic reason to have an FCA is to give Quark a Ferengi antagonist he could plausibly fear, since it's not like his bar is competing with any other Ferengi businesses on DS9.
But I still contend that the idea that there would be no FCA because the Ferengi would not want "big government" is projecting the particularities of modern ideological conflicts onto another culture whose conception of capitalism need not include such contemporary political biases at all.
ETA: The idea that "big government = bad" is not intrinsic to the capitalist ideology; it is a rhetorical device generated in order to justify preventing or dismantling legal mechanisms to alleviate or prevent the exploitation of the working class and economic inequality. In a capitalism without a meaningful workers' rights movement, such a rhetoric about the evils of big government might never develop.
in US politics, "big government" is indeed a simplistic rhetorical trick designed to short-circuit any discussion of higher taxes or programs that would help the poor or workers.
It is also most decidedly NOT the case that the more "unregulated" the market is, then the more social freedom there is or less authoritarian the government is. Authoritarianism and repressive social policies have often gone along quite well with neoliberal regimes, and more socially tolerant policies have often gone along quite well with more economically left-wing societies.
US politics gives a skewed perspective on the politics of the Left and the Right because of both a corporate-dominated media and because there really ISN'T a genuine Left in US politics at the national level that has any influence.