I suspect it has to do with accelerating the suction volume of fluid into the pump. If you simply had the discharge valve fully open and started the pump, it would quickly accelerate to wherever it is going to sit on its curve, set by the instantaneous hydraulics. That suction line of fluid needs to start moving and I suspect that could result in a low suction pressure trip. If you had a long enough delay on the trip, then the pump would get to its normal operating point and the suction would pressure would be at its expected value. However, I don't have any references to point you to.
Another advantage of starting with a partially closed discharge valve is reducing the load on the motor.