The load doesn't care about the sensing at all, if I set it to draw 10A it will draw it even if the input voltage is 0V.

Ofc, I don't recommend operating the load without any "voltage".
First you can't draw current from a zero voltage source with a passive non-source real load (read not a negative R). As you've shown the load is reading zero volts but the DUT source is 20 volts, so the load "thinks" the power is zero and shows such, but is really dissipating 200 watts (10A*20V), not 0!!!
BTW the power FETs know this isn't 0 watts but actually 200w and they will quickly see a temperature rise even tho the ET5410 is showing 0 watts, IMO this is not an acceptable condition!!
Can see that constant current load wouldn't care about remote voltage sensing as it's just sensing the current as feedback, and that's totally internal, but will get the power wrong as you've shown.
But, what about under constant voltage, resistance or power modes? Be careful here, without a schematic it's hard to predict what will happen if the voltage feedback is opened.
For example in Constant Power mode what could happen as Power is Current Voltage product, so measuring a unknown voltage could cause the load Current demand to rail if the unknown voltage is
intercepted interpreted as low voltage, yet the electronic load is actually "experiencing" a high voltage from the DUT source. This condition would likely quickly overheat & damage the load power FETs, and if the DUT is a high capacity battery even worse!!
Anyway, just trying to prevent/warn of a situation where one could damage the load and DUT. If we had a proper set of schematics then this could be analyzed, but without such as we said better to fail safe (2 resistors don't cost much)!!
Best,