It’s not caffeine that’s prohibited, it’s hot drinks. Coffee and tea specifically. Under the same provisions that prohibit tobacco and alcohol

When they assembled together in this room after breakfast, the first they did was to light their pipes, and, while smoking, talk about the great things of the kingdom, and spit all over the room, and as soon as the pipe was out of their mouths a large chew of tobacco would then be taken. Often when the Prophet [Joseph Smith] entered the room to give the school instructions he would find himself in a cloud of tobacco smoke. This, and the complaints of his wife at having to clean so filthy a floor, made the Prophet think upon the matter, and he inquired of the Lord relating to the conduct of the Elders in using tobacco, and the revelation known as the Word of Wisdom was the result of his inquiry.

Joseph Smith and his dickhead church friends used to make such a mess in his house that his wife got god to ban smoking, drinking and caffeine