The present-day political situation will be shaped, to large extent, by the history behind it.

Who developed the dragon-stomach smelter-generators first? Those people would have a significant advantage over others - the kind of technological advantage that could lead to the existence of political superpowers. Especially if there are few dragons left "in the wild," whoever got control of the breeding populations first is going to be the ones who arm their knights and men-at-arms with dragonhide equipment several plusses more powerful than everyone else's, their wizards with far more disposable wands of blow-enemies-up, and maybe even move ahead to larger-scale magical developments, like magical "engines" that can move their navy independent of wind and currents.

This could lead to political landscapes that parallel any number of real-world historical ones. Two or three major dragon-owning nations turning their smelter-generators to military development could create a Cold War-like environment, where most weaker groups ally with one side or the other to avoid being targeted by squads of elite troops wearing Helms of Teleportation, or by magical single-use city-killer devices. Looking further back in history, rival nations with access to dragon-refineries might get into a race to explore and conquer/colonize the world, paralleling the Age of Exploration and the concomitant colonialism. Finally, a single large power with superior magical "technology" might just conquer or annex their neighbors as long as it's convenient, then rest on their laurels for a long time, similar to some periods of ancient China and other large historical empires.

Personally, I think that the exploration/colonialism angle sounds highly likely. As people run out of "wild" dragons to capture and butcher/enslave, they would start to look abroad for new sources. Treating dragons as livestock would make wild dragons with desirable traits highly valuable catches, which would encourage adventurers to hunt them down. And, since transporting live dragons over long distances is no small feat, mage-engineers seeking more raw materials would set up facilities in colony towns or friendly/coerced foreign cities to enable them to process the dragons and possibly begin local breeding programs. After all, newborn dragons that have been Feebleminded since before hatching would be much easier to transport home for later breeding projects than their freshly-caught parents.

The next question is, what are the dragons doing about this? Dragons are, by default, highly intelligent, and live much longer than most humanoid races. The systematic enslavement of dragons as livestock is sure to be noticed, and few free dragons will simply sit around and wait to get captured or harvested. They would quite possibly have allies among the humanoid races, as the dragon-slavery system you described is quite horrifying on many levels, and many who realize that dragons are supposed to be sentient beings would be morally unable to tolerate their treatment. Abolitionists might seek to free hatchlings and heal the Feeblemind effects, allowing them to grow up free and sentient. Powerful adult dragons might manipulate or ally with humanoid populations that don't practice dragon-slavery, trying to create "safe zones" where they don't have to fear hunters. Truly ancient dragons might engage in guerilla warfare against enslaver populations - older dragons are high-level sorcerers in addition to their physical might, which gives them many options for ways to cause damage while putting themselves at relatively little risk. A great wyrm red dragon might have access to spells like Shapechange (for disguise purposes, among others), Create Greater Undead (which can create contagious undead, like shadows and spectres), or Sympathy + Cloudkill (congregate humanoids in a small area, then kill them en masse). Of course, this kind of thing would probably serve to convince much of the population that dragons need to be enslaved for the safety of mankind, but that's just part of what makes there be enough conflict to tell an interesting story in an RPG setting.

Anyway, it's an interesting setting concept, and I'd like to hear how you decide to flesh it out.