Absolutely! And you’re right that there are no large warrior nomad populations around to enlist… though it is possible to get a boost to your military strength if you can find a way to mobilize margin-dwellers like the Wiendish highlanders or Nyr reindeer pastoralists on a greater scale than the Hegemony has so far been able to. Still, the core approaches would as you note be taking over a chunk of the existing military and/or mass mobilization of some populous base group that supports your revolt.
COM does indeed cover organization and mobilization. Even at COM 2, I’ve written text like: “You put your well-honed command skills to good use, briskly organizing the nervous, somewhat reluctant villagers into teams with clear tasks.” That capacity will scale with additional COM points.
This is where, again, I think Karl Polanyi’s work is so important. Economic activity has never in human history been just about profit maximizing. This was an inescapable truth in pre-modern contexts, with abundant social restrictions on e.g. lending at interest, working on holy days, selling certain luxuries to certain classes, etc. If people had imagined a “private sector” back then, they would have taken for granted that its role was not simply to boost its revenues and cut its costs by any possible means. But even as we come to European modernity, where as part of the bourgeoisie fighting against monarchs and aristos you see the first emergence of the myth of an entirely autonomous and profit-driven private sector, the reality never matched the ideal.
Jump to contemporary America. Choice of Games LLC is a successful little private sector company. Is profit maximization CoG’s “entire purpose as an organization”? Absolutely not. Its purposes sincerely include promoting social justice and lowering “the bar for entry for the writing and game-design professions” through their royalty rates, HG imprint, etc. CoG didn’t pick those purposes because they thought that was the best way to maximize their profits; rather, they’re things that the founders, partners, and staff genuinely care about.
CoG also cares about making a profit; any company needs to have that as one of its primary purposes, or it won’t be much good at fulfilling any others. But companies that have that as their sole purpose are fewer and further between than you (or Milton Friedman and his heirs) might think. Making things well, or providing services well, is an intrinsic satisfaction for most people, not just something they do in the service of maxing out profitability. Loads of great companies succeed because they have a vision for what they can do/deliver better than anyone else.
Many companies have lost their way and failed because they lost touch with that, and started chasing short-term profitability at the expense of excellence, or took cost-cutting to foolish extremes that hurt their reputation and their clients. (And there’s no question that a certain flavor of right-wing ideology has worsened that damage by promoting market institutions that offer short-term incentives to reward short-termist thinking.) Still, most companies genuinely care about their reputation and following the law… both of which would constrain many service providers from putting raw sewage into the water supply!
When a company does something stupidly destructive like that, it’s wrongly reductionist to shrug it off as if that’s just an inevitable consequence of the profit motive at work. Not every company is an Enron. Most aren’t.
LIke I said above, much “public choice theory” applies a similarly reductionist lens to bureaucrats-- that they’re budget maximizers, always looking to preserve their institutional niche and boost the budget available to them by any means possible, whether or not it actually involves working for the public good. I’ve worked in a number of countries where local governments deliberately skimp on their spending on e.g. health post equipment or water treatment, leading to results similar in terms of cancer deaths and waterborne disease to what you describe.
But I don’t think those failures are inevitable, either. The principal-agent problem in public services doesn’t go away by treating either for-profit or non-profit institutions as inherently superior, but by careful (and usually iterative) design of regulatory institutions specific to the context.
Have you seen the Infinite Sea threads? We’re a quiet, sporadic little corner by comparison. 
We’ll see!