Oh I understand both the ramification of economic and military influence. But how does the Belt have the cards? That's absolutely not shown.
The largest concentration of Belters is just trying to get enough food and water. The primary fleet of Martian given and kit bashed ships of the Free Navy would have been destroyed, and if not they certainly don't have reason to go with Drummer.
Drummer's side of the Belt was seriously damaged, and the remains of Marco's fleet (at least his prong of the three) follows him to the ring gate where they are destroyed.
That really leaves Medina Station as the primary remaining mobile (though it hasn't been mobile for a while now) outpost. And it couldn't even stop the Roci by itself, a small martian fighter. How is it going to stand up to even one heavy cruiser from Earth or Mars.
And the Belters general work force is gong to be seriously hurt both in body count (as they are the only force on both sides of the war), and all the resources Marco stole from the colonies to fatten up the Free Navy. Much of that would be now gone. SO its not like they are going to have this fast large untapped labor force. Hell even with half of Earth dead, there are still more Earthers who need jobs, then the entirety of the Belt.
That's kind of the point; the belters aren't holding many cards at the negotiating table, which is why Holden and Drummer conspired to trick Earth and Mars to giving them some.
The reality is, yeah, what's left of the Free Navy can't stand up to even the broken and battered UN & Martian fleets. If they so chose, they could go back the the old days and grind the belters under their boots. But the cost to everyone would be ruinous. Earth and Mars needs the expertise of the belt and the resources of the colonies if they have any hope of surviving, let alone rebuilding, and if they double down on their oppression of the ever more desperate Belters, the whole system will turn into one giant prison camp and it'll be a pyrrhic war of attraction that could last for CENTURIES. By the end of it there probably won't be a civilization left worth talking about. Nobody wins in that scenario.
Remember that the fundamental cause of all of this is the rings. With access to over a thousand systems worth of resources, suddenly Sol System's outer planets are a lot less valuable. Which means a hundred million people suddenly don't have any means to support themselves because all the work has gone to the colonies. That leads to mass migration to the colony worlds for those that are able to adapt; a slow death for those that are not, and the utter annihilation of Belters as a culture.
The fear of that future where the belt is left to wither and starve and gasp is what drove people to Marco's banner in the first place, and with him gone, the problem itself still remains.
So to move forwards, they need to be given a future of their own. The UN and Mars were only willing to give them a one third share in their future. It might have worked--at least from their perspective--for a while, but it would have ended them all up right back where they started. One generation, two generations from now it'd all boil back up to the surface again. What Holden and Drummer did was make the Belt an intrinsic and vital part of human civilization, not just subjects of it. They will finally be able to build their own stations, free of UN or Martian oversight, or corporate control.
