When calculating the power dissipated by a npn transistor, Pq = (Vc)(Ic). Why don't we include the current in the bass as well? Why isn't it the following
You do. Its even slightly more complicated than that if the emitter is not at zero volts...
Look how LTSpice does it: Plot of the collector voltage, the collector current, and the power dissipated in the transistor as the base input voltage sweeps from 0 to 10V. Note the expression that calculates the transistor dissipation ( I didn't have to type it in; LTSpice knows it automatically).