Well as I understand it, the EPK is now just a dumb switch. It will never see LPFP pump load since it no longer provides power to LPFP, it just simply sends signal to a relay. So if the above statement from @jts1981's mechanic is correct, it would seem irrelevant what relay there is as the EPK would never see the LPFP power in either mechanical or solid state case. And again, this is for primary LPFP signal from EPK.
Essentially it does become a dumb switch. It will no longer see the load of the current from the pump. Which is why you can leave the fuse for the EKP stock. The EKP changes the duty cycle based on the lpfp sensor reading. For example, if the sensor broke it would run the pump at full tilt due to not knowing the output of the lpfp.
The voltage from the EKP is 12v. So when you start to turn on and off that 12v(through pwm/duty cycle), you can have a lower voltage applied at the pump, which is how it drives it slower.
With the relay now between the EKP and the fuel pump, the relay needs to be able to keep up with the duty cycle that the EKP operates at. A mechanical relay cannot switch on and off fast enough to be able to modulate the 12v from the battery to the pump so it will run the pump at full voltage from being stuck in the on position. But in the case of the solid state, it can turn on and off fast enough to keep up with the duty cycle from the EKP. So the solid state now will cycle the 12v from the battery at the same duty cycle that the EKP is telling it to do. Thus lowering the effective voltage at the pump.