I suggest you visit South America or parts of Africa and look at the wiring - the answer is yes, we do not need earthing at all,  but its not at a safety level we would normally accept, being single fault to danger.

Yep, its a shower, yep the red wires are carrying mains to it, yes the joins are just tightly twisted and taped. Its OK, just don't raise your arms up or turn the water up so high you get an unbroken stream.

UK wiring regs however have required earthing for new power circuits since 1939  (example of pre 1939  2 pin plug - plenty still in service during my childhood in the late 60s early 70s)  and lights since 1969 or so.

Mike

There's a good reason why the protective measure of electrical separation (such a s a shaver socket) is normally allowed to apply only to a single item of electrical equipment. Imagine an environment with no earthing. At some point a fault in a water heater causes the metal water pipe to come into contact with a live conductor (the N say). Perfectly safe, nothing trips, no one gets hurt.

Now imagine a year later, a kettle (in the same house or even in a neighbouring house) develops a short between its metal case and the other live conductor. Still no ADS. Now someone touches the kettle body with one hand, and a metal sink tap with the other hand. Instant death.

So it's good to connect all exposed conductive parts together so that a) they're all the same potential and b) something's likely to trip. Then, given that the ground around us is this big wet mass of soil and buried metal pipes, it's probably a good idea to bond that too, because it we don't do it deliberately, it's going to bond by accident anyway.

An isolating transformer with no connection between earth and the secondary winding only works well and reliably for a single appliance. It also gives some protection for a small number of appliances such as an appliance under repair and mains voltage test equipment used to facilitate repairs.

It wont give significant protection to the multiple loads used a house or a number of houses. In addition to the "two faults" scenario described above, consider cumulative leakage currents. A high leakage current on one wire would render the other dangerous to touch.

The risks can be reduced by use of a lower voltage to earth, such as the 55 volts to earth used on UK construction sites, or the 120 volts to earth used in the USA.