I always thought of current as the time derivative of charge, $\frac{dq}{dt}$. However, I found out recently that it is the ampere that is the base unit and not the coulomb. Why is this? It seems to me that charge can exist without current, but current cannot exist without charge. So the logical choice for a base unit would be the coulomb. Right?
Because it was defined by measurements (the force between two wire segments) that could be easily made in the laboratory at the time. The phrase is "operational definition", and it is the cause of many (most? all?) of the seemingly weird decision about fundamental units.

It is why we define the second and the speed of light but derive the meter these days.
