At take-off and in a go-around we require lots of power and thrust at low airspeed. For best effect we need both the prop and the engine to be operating efficiently.
Most prop blades are cambered aerofoils. This means that they are most efficient when their angle of attack is about 4 degrees. But at any given blade angle, the angle of attack increases as aispeed decreases. So a coarse pitch prop would have a very large angle of attack during take-off and go-around. This would make the prop very inefficient.
What we need is fine pitch to keep the angle of attack at about 4 degrees. To do this we select a high RPM, which causes the CSU to move the blades towards fine pitch.
Engine power output = Torque x 2pi x RPM. This means that for any given power output, if we reduce RPM we must increase the torque. But exerting a high torque requires the engine to produce high cylinder pressures. These high cylinder pressures tend to cause detonation. To demonstrate the effect of asking an engine to produce high torque at low RPM, try driving your car up a steep hill at low speed in fifth gear.
So in order to produce a large amount of power efficiently the engine needs to run at a high RPM.
So by selecting a high RPM we ensure that the prop is operating at an efficient (low) angle of attack and the engine is operating at an efficient (high) RPM.