When to use PID for motor control?
As always, what is your specification?

If the robot only has to move, and you are not too bothered about exactly how far, or whether in exactly a straight line, then a DC motor on each wheel simply switched on and off, or maybe speed controlled open loop with PWM, will do the job in the cheapest, easiest way. The assumption here is that the driver (human or some imaging computer program) is looking at the robot and correcting the next move command. With good DC motors, speed is well controlled by the terminal voltage, especially at low and balanced loads.

If you want a straight line, or exact distance, or profiled speed control, then you have a choice of DC motors with optical encoders PID closed loop, or stepper motors. Be aware that these only control the amount the wheels turn. If you want accurate wheel position to actually give you to accurate ground position, then your wheels must be perfect, equal diameter, running without slipping on a surface with no contamination.

It may be therefore that PID control of the motors is not sufficient to give a good ground position spec, and some form of geographic position sensing is needed. Once you have that, the need for closed loop on the wheel motors becomes less, unless you are trying to hit a very tight position/speed/time profile specification.

I'm not sure I understand what the phrase 'consistent power' means in this context, or why it should be desirable?