No, your reasoning is flawed
Stepper motors receive full power even sitting still (required to make them reach holding torque). This current is passing through the driver regardless what the stepper is actually doing. So the driver do heat up.
This is not something that applies only to the Xcarve but any stepper system out there.
So yes, it is entirely possible that the driver can overheat during “air carve” if its current limit is set too high or driver receive insufficient cooling.
Bottom line, the gshield poses a performance limitation - especially on the Y axis.
I fully believe your machine issues lies within the driver and/or rapid and acceleration rates - provided the mechanical aspects are sound
Does this change anything in machine behaviour?
If your machine loose steps without any grinding noise detected => most likely driver overheating
If your machine/steppers make sudden grinding noises (short bursts or prolonged) => mechanical or feed/acceleration issues.
Regarding Vref, check out this link for detailed information: