Why don’t B batteries exist? For that matter, we have AA and AAA batteries, but what about just A?
As battery powered devices were becoming more popular at the beginning of the 20th century, the types and sizes of batteries being developed were expanding. Around WWI, American battery manufacturers, the War Industries Board, and a few government agencies decided that they need to standardize. They huddled up and built specifications for the size of battery cells, their arrangement within the battery, their performance criteria, and other standards. This would allow product manufactures to designate a general battery model for their products, regardless of who made the battery.
Now that the standards and specifications were built, they needed to decide how to name the standardized batteries. For this, they chose to use the alphabet. They started with the smallest battery at the time and assigned it the letter A. They assigned additional letters down the line, finishing with D. There was a popular battery at the time that was called a Number 6, they elected to leave that name in place without adapting to fit the new standard.
As technology improved, batteries became smaller. With that, they introduced the AA and AAA models. These batteries found a great niche within smaller electronic items and caught on very quickly. With their higher capacity, C and D batteries continued to be popular for higher-consumption items. The usage of A and B batteries became less and less popular until they virtually disappeared.
But, although we never see them, A and B batteries do still exist for specialty applications. They can be found in some hobby packs or particular assembled electronics. Their usage continues to decrease, however, so we can expect that someday they will be completely discontinued.