Literally anyone can potentially have Ebola (unless you can develop an immunity to it, I don't actually know). Abominationhood is just a disease that a surprisingly small amount of the population is vulnerable to. Locking up everyone who might potentially contract the disease would be utterly insane and logistically impossible.
I would have thought the meaning was clear in context, but I suppose not.
Even people suspected of carrying Ebola, even if it hasn't outwardly manifested, can end up on the wrong (right?) side of a quarantine. Most people are not suspected.
You are right that a quarantine can become unsustainable if the population is large enough. This is why breaking a quarantine of can lead to a catastrophic pandemic, and so you want to quarantine when the suspect population is still small and manageable.
And it's here that I would say that national governments who are demanding that all magical defense of their nations be handled by the Chantry are shirking their responsibility to their own citizens and placing the burden of defense on keeping mages imprisoned... but I would prefer not to go into detail on that because the end of the Circle system would seem to make it rather moot. Though perhaps the Inquisition, if it takes over the responsibility for mages in Andrastian Thedas, will be able to answer these questions in-game, with rather more context and information than we have here.
Nationalizing the mages would be an epic disaster in the making and a horrible policy collapse. Internationalizing the mages was among the best possible things that could have happened for both mundanes and mages, and second only to allowing the mages to in turn dominate the international order the collapse of the international mage order would be one of the greatest steps backwards the setting could take right now.
The closest 21st analogy would be if we managed to create a viable, relatively neutral, collective space colonization program across the world, imperfect as it may be (let's throw involuntary colonization responsibilities and obligations on the participants who aren't allowed to return to Earth) but providing many public goods and services, and then decided to break it apart and let the nations nationalize whatever parts they could agree to (and get away with).
Or, alternatively, the current pending slow-motion balkanization of the internet. When nations switch from using national internet domains to creating their own self-contained intranets (arguably to circumvent US spying, effectively enabling their own domestic spying), the world is going to lose a precious commodity we take for granted today. There may even still be something called the internet twenty-five years from now, but it's not going to be anywhere as open or free as what we think of it today.
It may be useful to remember, indeed, that while Thedas is terrible in many ways, it's also substantially better in many ways than our own Europe was at a similar level of technological development.
It is also substantially worse. Medieval Europe only had the Black Death as the potentially apocalyptic factor: Thedas has the super-black death accompanied by its own hyper-breeding mongol hoard, along with abominations and ancient deities and a fully developed totalitarian ideology with an effective indoctrination apparatus.
By comparison, Europe just had the tyrannies of religion to deal with. Thedas doesn't even have that on a comparable scale.