EMC Cable shield used as PE wire, great idea or not?
The shield is not to be used as the replacement for the 4-th protective earth wire, your colleagues are wrong on that. The shield is just to prevent EMI radiation from VFD source.

Are there any other compelling reasons to use a ground wire?

Yes. Safety reasons.
If the VDF already has a filter, then it might be enough. The bearings are also consumable parts, or maybe that used motors are also very cheap and low quality, since they opted for wrong and cheaper cable VS. human lives.

The picture is from the Danfoss FC102 manual, without any doubt the cable has to have 4 wires. The guys who put a wrong cable are charlatans, dangerous people.