Half-cycling on the grid can be a problem for other devices than the one being half-cycled. The parasitic resistance in the pole-pig transformer and the wiring from it means you can end up applying a nontrivial DC component to the input power of other loads.
This DC component can result in a substantial current in the input winding of any transformer-powered device on the same circuit - or even the same drop. That, in turn, can result in the transformer saturating. Then its inductance drops a couple orders of magnitude and it pulls massive current until a fuse/circuit breaker blows (or it burns up).
If it's fused in the device, with a non-socketed protective fuse (as was typical for such devices, such as older hi-fi amps), it's "dead" until it's taken to a shop and the fuse replaced, at substantial expense. Then, when it's plugged back into the circuit near the half-phasing appliance it goes out again.
(You're unlikely to saturate the Pole Pig and explode it. Devices that could do that, like big motor controllers, are carefully designed to avoid exactly these issues.)