in SMPS when there is a difference between actual output signal and desired output an error signal is being generated. this error signal vanishes as soon as actual output reaches to desired output. so have doubt that how only proportional controller works in this scenario.
Study this .gif picture below: -
There are three phases in this little movie. Phase one just uses proprotional control to get the blue trace to align with the red dotted line. The red dotted line is the demand and the blue is the response to that demand changing at t = 0.
You should be able to see that with just proportional control, there is a finite error and a fair bit of overshoot. If more gain were used to "close the gap", it's likely that the overshoot would be sustained and you get an oscillator (undesirable).
Adding integral control gets the error down to zero but there is still a fair amount of overshoot. Addding differential control reduces the overshoot.
The above public domain picture taken from here.