Shorting plugs....

Do these really work well? And if they do does one need to worry about unused Balanced inputs?
That's not turning it off if it's a unit with a switching power supply (i.e., most consumer electronics these days); the only way to turn off such units is at the wall or unplugging them.

In any case, what was the configuration you used to test on since your current system can't accept more than one input? In addition, how close were the electronics to the system?
The Fisher 400c pre-amp shorts the input rca's that are not in use. Cool! This, from a 1950's design. I learned this from the schematic of the pre-amp.

I cannot say that this was progressive; I just don't know, but that is my thought. However, I can say that this was prudent design. It eliminates spurious noise from entering the active input signal path through cross-talk. And, that is the point of shorting your unused input rca jacks.
You'd best contact the manufacturer. Some products specifically advise against using shorting plugs.
I don't know why they would advise against it. I could understand against using them on outputs, but I am curious as to why they might advise against it on inputs.

I can see no reason not to ever use them. Either your input jacks are open or shorted with nothing plugged into them (based on their design, i.e. the input jacks on the Fisher 400c pre-amp). Shorting an input means zero signal in, no signal, no noise. Any rf spurious signal is shunted to ground. Only the live input is feeding the preamp input stage.

Still, I am curious...