In the mid 19th century people were becoming aware of the addictiveness of caffeine in the light of the emerging science of modern chemistry.[1] Joseph Smith took that trending concern and ran with it.

I don't know if Smith personally knew about caffeine as a specific component, but I think that was the background context--the mainstreaming of chemistry kick-started another cultural cycle of prescriptive living. The trend ultimately grew into the widely popular Clean Living movement in the latter part the 19th century, so Smith was way ahead of his time. See also Seventh Day Adventism and John Kellogg.

I don't mean to belittle the disciplines of the LDS church by putting them under a microscope. I just find the history interesting. Religious disciplines are obviously products of their environment, but that doesn't mean that's all they are. Anyhow, there's still good reason to avoid caffeine, depending on your priorities and concerns.

[1] Doing some Googling to confirm my memory and that I'm not completely talking out my a--, it seems caffeine was first isolated in 1819. The Clean Living movement (which I didn't remember by name until Googling), was later than I seemed to remember.

That's very interesting of course, and explains the history, however it's been well over a century now since this stuff, so people should know better about relative safety of different foods and not just stick to what John Kellogg said. We see here that the Mormons are now OKing soda, which wasn't around in the 1800s, despite us now knowing just how horribly unhealthy it is, yet they don't want to reverse their stance on tea, which has been used for many centuries starting in Asia and later spread to every corner of the planet, and isn't really associated with any significant health problems (in fact, green tea is consumed in large quantities in Japan, which has the highest life expectancy in the world).