Can I drive a stepper motor with a regular MCU?
Yes, an ordinary MCU would be sufficient to drive a stepper motor, in a 'dumb' way.

Many special purpose stepper motor drive chips do more than generate the appropriate step sequence to energise the stepper motor coils. 

So special purpose stepper motor drive chips are not equivalent to an MCU with some power switching.

For example, some stepper motor driver chips will drive the stepper coils with constant current from a higher voltage than the stepper is rated. This allows the stepper motor to achieve better performance. Using a 'dumb' stepper sequence and dumb power switching with an over-voltage power source would likely overheat and damage the stepper motor.

Also, some stepper motor driver chips will handle microstepping, which gives smoother movement, and could avoid or minimise stepper motor resonance.

Stepper motor drivers are also likely to protect the motor from excessive current draw if it stalls.

It would be possible to use a MCU, with enough resources, to achieve all of these things too. However the complexity of the electronics is well beyond power switching. Also the complexity of MCU-based software to achieve comparable performance and robustness would take a significant amount of time to develop (from scratch).