Sirius and Gallia contains well over a hundred billion humans - and growing - growing exceptionally if you realise that there were only a few million eight hundred years ago, as there's been no resource on human growth that has required a population slowdown. Many of them own spacecraft, and most spacecraft have some degree of defensive munitions due to massive organised crime and terrorism on a scale which isn't imaginable on Earth, due to largely uncaring governments, even in houses like Bretonia, which is possibly the most ethical house of them all.
There are probably tens of millions of nomads, perhaps they are legion throughout the Daam K'vosh hypergate network, but millions is not enough to destroy a well-armed humanity that has shown an ability to unify against common existential enemies and does so frequently (look at Gallia and how it's brought disparate people together).
Why not make humanity destroy itself? For a thousand years, humanity has engineered the tools to destroy itself - first hydrogen bombs, now antimatter and even singularity weapons. Why not push that instinct, always there, but suppressed by morality, over the edge with targeted paranoia and false-flags through their Wilde thralls, then clean up what remains?
In addition, the Nomads are growing in strength, and can adapt to human countermeasures against them faster than humans can adapt to the nomads. Tactically there is no victory for mankind.
THE SYNDIC LEAGUES
(A co-operative of Rheinland's Shipping Unions, retired from a life of piracy.)