Only in your dreams, not in the real world.
Yes, you are right.
And now problem could be with any one of the six to twelve circuits and the utilization equipment they supply.
Lets say the its the defrost circuit on the basement fridge. It only happens sometimes when the unit goes into defrost. How does the electrician narrow this down in one stop? The clock $ starts running as soon as I am heading to the call.
This is the problem with using a single sensitive device on multiple pieces of a equipment.
It is a real problem, not an imagined one. It is the same problem electricians and home owners have with AFCI troubleshooting and you want to compound this by tying more equipment to one device.
That is not a step forward, that is a step in reverse.