What are you referring to when you say “salt batteries”?

This is more accurate than you would think. I’ve seen people synthesize a new inorganic compound, and is then more or less forced by supervisors to test it as an intercalation host for Li- or Na-ion batteries without really having thought through whether that makes sense at all.

Li is small, and as long as there is room for it (sites for it to sit when intercalated and paths to diffuse through the material), and there is some species that can accommodate the additional charge (as one Li+ is introduced into the material, there needs to be a charge compensation to maintain charge neutrality - typically this is a transition metal cation that is reduced from a higher oxidation state to a lower one). In that sense a lot of materials could serve as hosts, and depending on the intercalation potential, it could be used as a cathode (LiCoO2 for instance, where the intercalation potential vs. Li/Li+ is so high that it makes for a good cathode) or an anode (LTO for instance, where the intercalation potential vs. Li/Li+ is so low that it rather makes sense to pair it with a high potential cathode, and instead make for a more niche application where things such as safety is more coveted). That said, only three structure types have been widely used commercially as intercalation hosts for Li-ion batteries: layered rocksalt types (like LiCoO2 and its deriviates, NMC and NCA), spinels (LiMn2O4 or LTO) or olivines (LiFePO4, or LFP).

Li-S is not someone randomly mixing Li with some other elements though, it has been researched for a long time and is considered one of several “holy grails”

In this case, C refers to the current rate, not the unit Coulomb. It is a standard way of giving the current rate in battery research, and 1C is defined, as oldfart says, as the current rate required to charge that particular battery fully (to its nominal capacity) in one hour. 2C is twice this, so it is charged in half an hour, and C/2 is half this, so it is charged in two hours.

It is a convenient way of giving the current rate, because it allows a more application focused comparison (i.e. my EV battery or phone battery should be able to charge fully in one hour), but it hides the actual capacity of the battery (you have no way of knowing, without additional information, if the cell has a small or a large capacity).

ETA: The last point here is what deranger and AwesomeLowlander is getting at. You can have a very small battery with very little active material, and charge that at 10C and achieve reversible cycling for many, many cycles, and it is meaningless if it cannot be scaled to a larger cell (unless we are only considering microbatteries for example). Usually, results at a small scale is not directly transferable to larger scale, and you encounter all kinds of challenges as you scale up.