Canon factions like the Republic and the Sith obviously have a great advantage. After all, when all is said and done Star Wars is about Jedi vs. Sith (hence why the Republic tends to look like the Jedi Order plus a couple senators and NFU soldiers in actual member base since everyone likes to be a mage...saying this as someone whose main is one, not being hypocritical at all!).
However, with a sufficiently dedicated member base that's willing to try out new things noncanon factions can be successful. The best cases are the Omega Protectorate, which back in the day went a long way from its humble beginnings as the paramilitary mercenary organisation Omega Pyre to a full-blown merchant republic that in its heyday was one of the three big powers, and presently the Fringe Confederation, which went from being a band of people who did not fit into other groups and were gathered by the ex-Empress to battle monsters in the unknown regions to one of the most powerful empires on the map that can take credit for halting Freedom Train.
@[member="Delila Castillon"]
You know I'm always down for doing Rebellion stuff when the opportunity arises!
On a more serious note it's true that minors have difficulty drumming up sufficient support, especially over a longer term, though that also depends on the group. For instance, the Army of Light had a great premise and good ideas, but it lost its main reason to exist as an independent group when the Jedi went on their own anti-Sith Crusade.
People do want their conquests, saying this as someone who likes claiming planets, causing mayhem on the map and whose presently only faction identity for Siobhan is a minor one, namely the Kaeshana Confederation, because while there are some majors she might like (she would...make a good Mando) to an extent Kaeshana is where she belongs IC wise. Admittedly the space elves one day rising up and going on a conquest spree to subjugate the humans would be fun...but, yeah, not feasible! Like while Moira is affiliated with Fringe the only cause she espouses is the Age of Steel Archangel (presently a corporation, not a minor faction, but then she secretly works with one of the Sith minor factions, a nonstate actor, who could potentially cause a great deal of chaos) pursues, with the aim of becoming an NGO Superpower, and it's been plenty of fun, not to mention led to some rather original plots, what with two assassin droids plotting to usher in a mechanical dystopia by climbing the corporate ladder and all that.
After all, one does not have to possess a big space empire to influence things. A confrontation between the Republic and one of the minor Sith factions, a nonstate actor that operates without regard for borders, commands considerable resources but does present a visible target in form of planets that can be conquered, would be fun ('super-empowered darkside extremists strike at the fortress of freedom'!).