Why is current (and not charge) an SI base unit?
It's about what was a measurable quantity in the late 19th century. Counting ~1019 electrons would take a long time, but it's "straight-forward" to measure the force two wires exert on each other.

Also, consider that electric current was well-known and widely-studied for many years before the existence of electrons was known and their charge was measured. I don't know a date for the first observation of electric current, but Ohm's law was published in 1827, while the electron charge wasn't measured until 1908.

Since they were first established, we've changed our choice of fundamental units very little, and only as improved measurement technology has come along. At the moment it's still considered easier to measure the force on parallel wires than to count quintillions of electrons, so we still consider the ampere a fundamental unit and the coulomb a derived unit, defined as an ampere-second.