Lithium ions have a relatively low conductance (Wikipedia) so why are they used in batteries, and not sodium, potassium, etc.?
The conductivity values you cite are for ions in water. there is no water in a lithium battery otherwise, it would explode and burn before leaving the factory. Beside low conductivity can be compensated by increasing concentration of the ions or a variety of other architectures.
Further, there's a few reasons lithium is optimal in batteries. It's not environmentally toxic (like beryllium), has a higher oxidation potential than the other alkali metals, but most importantly is its high energy density in both Joule per weight and per volume, as well as power per weight, which no other metal can beat. The only disadvantages for lithium are its flammability and cost.