Well, for reference Elistra I is very much like the Capital Planet of the galaxy. Historically, it has been an important centre of political, military and economic power for a long time. And Elistra II and IV, I guess (the one denoted as III in the story until I fix it) have, too, been important planet throughout time. They (in fact most planets mentioned here) were originally during the first millenium AF, Figoranol planets, but after the fall of the Figorani, the other peoples of the galaxy made their own homes there and continued to thrive.
But even if you don't account for that the fact is that Elistra I alone has an entire planet's worth of a fleet when the Nexus Force's numbers are doubtful to reach any close to that of a planet's seeing as they are based on only a small part of the Crux System and are founded relatively recently. But even as equal forces, the NF is already busy dealing with the Maelstrom and thedude, so an attack from Elistra would tip the balance very much against them.
As for Danvaria, it is left to be assumed by the reader, though indeed it's not that clear that probably through a victory it had in the mentioned Third Great Galactic War 300 years ago made the other planets agree to compensate it in case of another war. It has no real control over them and that's why the Empress threatens them with an embargo as punishment if they do not do as they say. Jirdia, however, is said to be Danvaria's protectorate, with Danvaria's protection possibly allowing them to have that kind of peace they need to 'eradicate crime'.