What determines the speed of charging of a battery?
There are many factors limiting speed of charging. Here are just a few:


Run-away overheating -- some battery chemistries, such Li-ion, may even self-ignite.
Spalling of electrodes -- the physical stress of rapid charging can buckle electrodes and cause a composite electrode to break apart.
Side reactions -- to increase the charging current, higher voltage is required. This over-voltage causes undesired side reactions, such as lithium plating (and out-gassing in Ni-MH and lead-acid batteries).


To make cells charge more rapidly, each of these potential issues must be analyzed and both the cell and the charging system must be designed to overcome the problem. In some cases, there have been spectacular failures, even when millions have been spent on design.