This too will run at very low flux levels.
If its designed with enough turns and core cross section to run at 240 volts RMS, running it at (say) 12 volts RMS, both eddy current and hysteresis loss will be extremely low, as will the magnetising current.
The core losses would probably be down in the milliwatt range I would think.
The only real objection to the idea that I can see is the size and weight of the toroidal transformer for what it has to actually do.
But if its free, and we are only building one of these, as an in house calibrator, its not a bad solution.
Once its properly calibrated, only the current in the primary needs to be controlled with current feedback.
There is no mechanism whereby the current transformer ratio can drift or change.
Just a 100mA current shunt to ground in series with the primary (10 ohm resistor) and loop that back to the inverting input of the power amplifier, and that is it !
This naturally assumes a 1,000 turn primary.
But whatever the actual turns ratio turns out to be, its just a simple case of tweaking the current shunt and initial sine wave drive voltage to get the desired 100 Amps.