I don't see AFCIs being very effective on any wiring system that does not include an EGC. It appears to me that most of the trips are from the ground fault circuit and not the fancy arc signature circuit. The GFP trips with a 30 to 50 mA fault, the arc signature circuit doesn't even look for faults with currents less than 5 amps.
Ground fault protection works on ungrounded circuits so the EGC is not required but does improve the performance of GF devices. To my knowledge all GF detection works by totalling the current out and the current returning. they must add vectorallyl to 0 or within the trip setting of the device 6ma for GFCI and Usually 30ma for a GFI device.
The series arc detection requires around a 5 amp threshold and arc signature. That may not have very much GF leakage and I suppose if the parallel arc detection is phase to phase you could be correct about not working without the arc signature. The fact that the current might travel through the studs or other path will activate the GF protection even without the EGC.
