In fact, there was a Science Versus podcast about the benefits of lithium in public drinking water. Lithium naturally occurs in some water sources more than others, and areas with more lithium in the water have better mental health.
(To answer myself, from Wikipedia..)
>Common side effects include increased urination, shakiness of the hands, and increased thirst.[2] Serious side effects include hypothyroidism, diabetes insipidus, and lithium toxicity.[2] Blood level monitoring is recommended to decrease the risk of potential toxicity.[2] If levels become too high, diarrhea, vomiting, poor coordination, sleepiness, and ringing in the ears may occur.[2]
Plus they are already pretty recyclable unlike plastic. Really lithium is probably one of the 'cleanest' materials we've had for batteries given that they aren't mostly heavy metal like NiCad or Lead-Acid.
There is quite a bit of R&D going into negating the need for Cobalt in Li batteries. I would not expect Cobalt to be needed in ~3-5 years (for Li batteries).
The tl;dr is slightly lower energy density (~14%) in exchange for non-toxicity, extremely low self-discharge rates, not prone to runaway thermalling, and great cycle life.
It also has the advantage of being able to be essentially a drop-in replacement for many lead-acid uses.