> The only reason they run separate wires is in case of of mistakes.

Erm no.

1. In case the neutral gets disconnected, so the frame isn't at the potential of the hot (no voltage drop across the device)

2. So the return voltage drop in the white wire isn't on the body of the device. ~20 volts between adjacent high-current appliances on different phases probably wouldn't be terribly dangerous to most people, but it is sloppy.

3. For GFCI/RCD, it separates bona fide return currents from "accidental" return currents. With only two wires, dropping a toaster into a (PVC-drain) bathtub wouldn't trip. (Erm, I just realized most toasters are actually only two wires. Well uh, don't do that).

If that "toaster circuit" is protected by a GFCI, it will indeed trip with only two wires. The GFCI is sensing the imbalance between hot and neutral (the rest went through the bath water). Both currents pass through the same toroid, but they are in opposite directions and normally exactly cancel, so no flux is induced in the toroid. If there is an imbalance, a current is induced in a secondary winding. This will trip the GFCI internal breaker. Note that this does not involve the green wire.

Except there will be no imbalance if there is no other path for the current to travel by...

The geometry of the electric field in water should probably be similar to that in air (mostly contained to within the case), just don't drop both a toaster and a waffle maker in at separate ends.

The resistance of slightly salty bathwater is much lower than air. While baths are not often plumbed with metal pipes these days, one can still expect some current flow to ground. It only takes milliamps of stray current to trip a GFCI.

Milliamps sounds like a tiny amount in the context of home power, but 5mA at 120V is still only 24kOhm. This is actually pretty low to just assume away. I'd agree there could be some water left over in the drain pipe from the last bath, splashes making a path to the spigot, or something like that. I just wouldn't count on it.

Iirc gfci's are nec code allowed on non grounded lines because they will still trip, but you have to test with the gfci test button because they're only tripping on current difference, not like a breaker.

Yeah, IIRC the "proper" way to upgrade an ungrounded circuit to have a 3-prong outlet (without running new cabling) is to use a GFCI and label it "NO EQUIPMENT GROUND". This is considered safe, but is still ultimately a hack.

It assumes that any dangerous shocking current will be taking a path that isn't just coming back on its own white wire, presumably from taking an unspecified path to ground. This seems a reasonable assumption for safety (and the NFPA surely has looked at the data), but it doesn't really inform the above isolated-bathtub situation.

There is also the matter of unanticipated leakage current between hot and the equipment enclosure. The EGC/green wire keeps the enclosure close to ground potential.