How does the buck regulator soft start condition reduce the unwanted voltage drops from high impedance power sources?
During startup, a buck converter without soft start will attempt to charge its output capacitors as quickly as possible.  The control loop will likely saturate causing the regulator to put out maximum duty cycle.
Since I = C*dv/dt, that means a large current to charge the caps.  If your supply to the buck converter has a relatively high impedance the large inrush current could cause the input supply to drop in voltage, potentially causing other parts on the same rail to reset or brown out.
By controlling the start up of the buck with a soft-start, the &quot;dt&quot; term is longer so the inrush current is lower.