In a modern, developed country, where we suffer very few of these contagious diseases, it’s difficult to appreciate just how terrible they are. Smallpox was an extremely contagious, miserable disease, and mortality rates were as high as 30%, leaving many survivors disfigured or blind. It has quite literally been a scourge on humanity for centuries.

One reason the vaccination movement was so successful globally was because in the 60s and 70s, the World Health Organization, supported by the United States and the Soviet Union, put a huge amount of money, time, and personnel into eradicating the disease. Your description of the modern smallpox vaccine describes a much more medically difficult experience than most people went through. And while there were adverse reactions, higher than for other vaccines, the broad consensus of health professionals and the public was that these were far less important than eradicating smallpox.

Smallpox was a miserable, disfiguring disease with a high mortality rate and there was every reason to want to eradicate it, The vaccination process isn’t as horrible as you’re describing, there was a major, well-funded global effort to destroy the disease, and the chance of adverse reactions to the vaccination was considered far less important than eradicating the virus. Finally, the anti-vax movement was not nearly as widespread and widely supported by popular well-funded people in the media, and they didn’t have the platform of the internet to spread that message.

The NIH has a great, readable article on the history of smallpox vaccination:

Belongia, E. A., & Naleway, A. L. (2003). Smallpox vaccine: the good, the bad, and the ugly. Clinical medicine & research, 1(2), 87–92. doi:10.3121/cmr.1.2.87