Because the only full-blown cases of smallpox came from people who developed it as a consequence of the vaccine. At least for a period after 1980, there was a standing reward of $10,000 for any naturally occurring case of smallpox.
In terms of how the world would respond: strategic reserves of the smallpox vaccine are kept in various places; it is still provided to the US military due to its presence in weapons stockpiles, and defense prioritization and funding would be put to work in the event of a suspected weapons-grade outbreak.
Because the only full-blown cases of smallpox came from people who developed it as a consequence of the vaccine.
Presumably there's an implied 'after X' where X is long after smallpox has been perceived to be endemic.
This is the correct answer AFAIK - several lab leaks of smallpox samples after eradication caused most of the remaining samples to be consolidated into a few secure locations.
Also, the US military is not the only military to vaccinate; some countries can also give their soldiers injections without officially saying what's inside them.
I was wondering about this too -- smallpox may be eradicated for now, but it is often mentioned as a top potential bioweapon (its genetic sequence is available, etc), plus the other possibilities you mention. So it seems crazy that our anti-smallpox preparations are pretty minimal. The US government claims it stockpiles enough vaccine for everyone, but they said the same thing about the national PPE / facemask stockpile, so I'm inclined to doubt that there could be a smooth rollout in an emergency (rather than, eg, discovering that many of the doses have spoiled, or running out of key secondary components like needles). It also struck me as odd that vaccination is impossible for ordinary citizens to get voluntarily, despite being mandatory for members of the military.
But when I looked into the details, things started to make more sense:
-The immunity created by the smallpox vaccine only lasts 3-5 years before beginning to fade. In modern society, it's not just young people who lack smallpox immunity -- it's everyone. Changing that would require giving shots every ~5 years, which is a significantly bigger effort than a once-in-a-lifetime shot.
-The smallpox vaccine is based on somewhat primitive tech -- it uses a live pox virus (not smallpox itself, but a less-deadly relative) and is administered in an odd way. Side effects of smallpox vaccination are more common and more dangerous than for most vaccines, such that vaccinating everyone in the USA would lead to several hundred deaths. (Repeat every five years!)
Even with up to ~1000 deaths per vaccination drive, this would plausibly still be worth it on utilitarian, longtermist grounds, considering the threat of smallpox as a global catastrophic biological risk. But there would be significant downside, so it's very understandable why we don't do it.
IMO, seems like these two things could improve the situation:
-we could allow private citizens to get the smallpox vaccine voluntarily (as seems to have been briefly considered in the years after 9/11). This would be an easy way to make civilization more resilient while offering folks incrementally more freedom, although there would inevitably be stories about a handful of people getting sick or dying from the vaccine, which might unfortunately reduce public trust in all vaccines generally.
-It would be great to have a more modern-style vaccine that's less dangerous. If we could create a modern smallpox vaccine using a platform like mRNA, this would also mean that we could more quickly make huge numbers of doses in an emergency (since we could use every mRNA factory instead of being limited by the custom pipeline for the current vaccine), and we could easily change the vaccine to handle variants -- especially important if we are trying to fend off a bioweapon with a deliberately modified genome. I don't know how much designing and testing a new smallpox vaccine would cost, but some scientists have called for preemptively creating at least partially-tested vaccines against every major virus family with pandemic potential, to give us a head start on future crises, so it's certainly not outside the realm of possibility.
If an adversery creates a small pox bioweapon, there's a good chance that they would try to mutate surface proteins of the small pox vaccine to make it evade a commonly used vaccine by the enemy. Preemptively, vaccinating against possible bioweapons doesn't seem to work.
The eradication of smallpox in 1979 represented one of the greatest achievements of modern civilization. However, since then most countries have elected to stop vaccinating their populations against the disease. This seems like a very concerning vulnerability to me, with waning herd immunity due to more and more of the world's population being replaced by unvaccinated young people.
What if there was an unintentional release from one of the labs around the world that still hold on to samples of the virus? What about an intentional release by terrorists/rogue nations? What gives scientists the confidence that there are no undiscovered animal reservoirs or uncontacted tribes in remote places where smallpox is still circulating? Smallpox is highly contagious and hundreds of times more deadly the SARS-Cov-2.
How would the world respond to such a release? Is there enough capacity to rapidly produce and deploy billions of doses of smallpox vaccines? (Right now we're at an all-time high in terms of pandemic preparedness; I'm thinking decades down the road when the lessons from Covid-19 has been all but forgotten)