Also, for stories about Ferengi Corporations to have much impact on the Feds, the Feds would themselves have to still have a normal capitalist economy too. The replicator and the "No Money" thing really cut off the potential of the Ferengi.
Ferengi Corporations could still have had an effect on the Federation even though the Federation doesn't have a capitalist economy.
If a Ferengi Corporation was dumping toxic waste on a Federation world, that would affect the Federation. If Ferengi corporations were trying to influence galactic trade policies and were campaigning against other civilizations joining the Federation because they didn't want them to join the socialist economy of the Federation, that would effect the Federation. The fact that the Federation still trades means Ferengi Corporations can try to get influence, they can always try to corner the market on something the Federation wants.