Why does a BJT transistor require detailed calculations for its base resistor value to operate?

Answer: Because of the role the base region play in the transistor.

Explanation:

The base region of BJT transistor - an opposite polarity charge carrier from emitter region to collector region, plays a vital role in triggering for a sufficient emiter - to - collector current.

The current received by the base region of BJT determines the effect of the continue flow of current into the collector region which will eventually determine the output current.