I cannot think of another vaccine that we would willingly inject into ourselves (or our children) for a disease for which you have an enormously high statistical chance of having very mildly.
You want to know another disease for which people have an enormously high statistical chance of having very mildly? Polio. Most people who got it were asymptomatic or only mildly ill. But because some died or were permanently disabled, and because the virus was so contagious that huge numbers of people caught it, that still meant a very large number of deaths and people with permanent disabilities, and a vaccine was vital.
You want to know another disease which is usually mild or asymptomatic? TB. About 90% of people who are infected with it have no symptoms, and many of the others will have mild well-resisted cases. (My mum almost certainly did as a child, and she lived to be 96.) If you have an impaired immune system, it is much more likely to become severe or fatal; hence the advent of HIV made TB more of a threat. But, even without HIV, it is a serious threat, making a vaccine and other treatments vitally important, because it is so contagious and affects so many people. Even if the majority of people with an infection are not seriously affected, if 25% of the world's population has it (which is the current estimate for TB), it means a lot of serious and fatal cases.
By contrast, SARS has serious effects on a much higher proportion of those who get it, but because it's much less contagious, it was possible to get it out of circulation without the need for a vaccine.
What makes a disease serious, and the need for a vaccination important, is not just the severity and mortality rate among those who catch it, but those things combined with the number of people who do catch it.