Too small a conductor and/or a conductor run high above the ground or through areas where flashover could damage sensitive or expensive stuff.
I also consider auxiliary electrodes (permitted but not required by the NEC) to be 'unwise' in general, unless proven otherwise in the specific case.
The case in point which brought this to my attention was the (stupid, since removed) 2014 NEC requirement for an auxiliary electrode for rooftop solar arrays. This essentially required that a combination of EGC and GEC be run
over the roof and through equipment and ultimately connect two remote electrodes, where the EGC could also be as small as 14awg. Mike Holt explained at length in this video why that is a bad idea, see illustration around 10:20 in particular.
My belief is that if you have two widely separated electrodes that the NEC requires be bonded, the best practice would be to bury the bonding jumper in the ground outside the house, or at least run it through non sensitive crawlspace or basement area underneath the house. 'Unwise' in lightning prone areas would be through the middle of the house or over the roof. Or like, through the server room of a commercial building.