Linux Mint downloads (briefly) compromised

you are ignoring one factor. how many people catch measles vs how many you are vaccinating.

Measles have a contagiousness index of 0.98, which means that if you're unvaccinated and exposed to the virus you're virtually certain to be infected. (The highest possible value would be 1, which means that everybody who is exposed is infected.) Not everybody who is infected with something actually shows symptoms – the “manifestation index” specifies how many people who are infected do exhibit the symptoms, and in the case of measles this is around 0.95.

So obviously the thing to do is to avoid being exposed to the measles virus in the first place, which is why vaccination against measles is so important. If most people in a community are vaccinated against measles, the resulting “herd immunity” means that the measles virus can't obtain a foothold, and this protects even those people who can't be vaccinated because they are too young (you have to be 1 year old or so to be vaccinated) or their immune system doesn't work as it should. Anti-vaxers can often get away with not vaccinating by hitching a free ride on herd immunity, and that creates the illusion that “I don't need to vaccinate because in reality nobody actually ever gets measles, it's all a scam by Big Pharma”. This goes wrong when there are too many anti-vaxers bunched together. For example, here in Germany measles outbreaks, if they occur, often occur in and around Steiner schools, where anti-vax is a big thing and there is no herd immunity.

The reason we don't see many measles cases in the Western world these days is that widespread vaccination has pushed the disease way back compared to, say, 50 years ago. The measles virus has no non-human host so in theory it would be possible to eradicate it completely like the smallpox virus or (almost) the polio virus, but we're not quite there yet; the fact that it is so contagious doesn't make things easier, either.

If you have something that one in 10,000 people catch, and the vaccination has a problem 1 in 1000 times, it is a net loss, even if the disease is 100% fatal if someone gets it without the vaccination.

One disease which is almost similar to what you're describing is rabies, which is why we don't vaccinate everybody against rabies on the off-chance. Rabies is pretty rare in most places, but there is no cure – if you do catch it you're practically certain to die from it. The rabies vaccination isn't problematic in the way you describe, but it is a very unpleasant experience (though way less unpleasant than the disease itself, and it does have the considerable advantage that in the vast majority of cases it won't kill you like rabies does). Fortunately you can still get vaccinated against rabies after you're exposed to the virus but before you start exhibiting symptoms, so that is the usual approach.