For any signal cable that is not a differential signal, if you connect it between two devices that are both grounded, there can be an unmatched flow of current through the cable. And coiling such a cable would increase the impedance of the cable. Even then, signal cables usually don’t carry enough current to cause any over-heating issues, but the greater impedance could degrade the signal.
In practice, such a setup is susceptible to ground loop, with or without a coiled cable, so it’s best to avoid anyway. Most high-speed digital signals (e.g. ethernet, USB) use differential signals over paired wires, so coiling the cable shouldn’t be a problem.
It is interesting to try to find power cables that are not run as a balanced pair. They are hard to find. Domestically, looking around the house, there are none. Everything has both legs. Inside the house wiring you will find the odd single core cable - they get used sometimes with double ended light switches, but even then tend to be routed along with their brethren.
Car electrics is the obvious case where power tends not to be run as pairs. The car chassis is used as one leg, allowing power to be run with a single cable.
It is really worth re-emphasising the point continually made, and then ignored, about the nature of the magnetic field from a conventional power cord. For all useful intents there isn’t one. The field from the two conductors cancels out. But the myth that coiling up ordinary mains power cords causes issues due to increased magnetic/inductive effects seems to persist.
Years ago I was on a compulsory electrical safety training course, and the guy teaching the course was adamant that this was the case. The fact that he was presenting the course to a room full of university scientists who tried to set him right didn’t dissuade him.
With the exceptions that Francis Vaughan notes, it is rare for any cable to deliberately carry unbalanced current. If you do somehow end up in that situation and you coil the cable, then you’ve effectively made a common-mode choke. This increases the common-mode inductance but keeps the differential inductance roughly constant, generally reducing the unbalanced current. That effect will usually be negligible without a core, though (like the ferrite cores used in this way to improve EMC).
The only reason not to coil any kind of signal or power cable encountered in typical daily life is heat. The biggest example of deliberate imbalance, in automotive wiring, is DC: so there’s no time-varying field, and thus no potential for interference. That’s presumably not by accident.