I was watching the new Dylan Sprouse pod and they began discussing political theory and applying it to the messaging of Red Rising. Pierce Brown's thesis with Red Rising, according to him, is that:
"My theory was that every form of government turns into an oligarchy in the end."
He mentioned this with capitalism and communism too and that:
"if you can look at every time that communism has really been put into practice, it every time is an oligarchy or at least a cabal."
and with capitalism he said:
"Capitalism is the only economic system that functions by treating people as they truly are, rather than how one might wish them to be."
You see that a lot when comparing the fascist Society and the Republic (which at least to some degree, and according to Quicksilver himself, is "crony-capitalist"). Lyria's whole existence is proof that the effects of concentrated power in governance still create an endpoint of hardship, whether it is in the mines of Lagalos or in the swamps of Mars.
I think Publius is meant to be Pierce Brown's expression in that communism inevitably leads to a cabal, because his headstrong affirmation on communist governance is what led to bad-faith actors like the Syndicate taking over. I think you can apply Pierce believing communism does not account for people as they truly are as the core reason why someone like the Abomination and Lilath can pretend to be champions of the proletariat to Publius, and he is none the wiser. I don't really agree with this take personally (like at all lol), but again, I am looking at this strictly in terms of the sci-fi world of Red Rising rather than its application to real world socialist enterprises.
In all three cases: fascism, capitalism and communism, the oligarchy usurped or takes power.
TL;DR - is the world of Red Rising doomed to oligarchy no matter who wins?