But as 3rd Earl says... don't the brass connecting screws in effect
make an earth connection from the brass faceplate to the metal back
box, to which is connected the supply earth. Same as a flying lead,
really.

Not reliable enough. You want the secure connection to the faceplate and the
dodgy connection to the backplate. The screws rust and can end up with a
high earth impedence. In the event of an earth fault, this could be high
enough to cause a fire. Unlikely, I know, but not best practice.

I always turn the power supply off before I unscrew any switch face
plates.

I don't. Nor do many others. I might want the lights on when decorating
behind the faceplate.

Christian.