[TonyDuell]

I can see no point at all in having an isolating transformer and then connecting one side of the secondary to earth all the time. Since mains earth and neutral are bonded together on the incoming feed to my house (PME installation), the isolating transformer would seem to add nothing.

Of course there will be times when one side of the secondary does end up earthed A common example is if I am working on a typical AC/DC radio, powered from said transformer and I clip the earth lead of my 'scope probe onto the chassis. There's a connection from one of isolating transformer output wires via the 'neutral' wire of the radio's mains cable, radio chassis, 'scope probe earth lead, 'scope chassis to mains earth. But that's why I have an isolating transformer, so I can make that connection without tripping the RCD in my consumer unit.

And if I have a radio where there's a bias resistor between the neutral mains lead and chassis, I can earth the chassis without removing the bias from the valves. Or more typically I'll be working on some kind of switch-mode PSU which starts by bridge rectifying the mains. With an isolating transformer I can earth the -ve output of the rectifier without effectively connecting a diode across the mains (== blown fuses and diode hitting the ceiling)

High voltages are dangerous if mishandled and I do not believe for an instant that an isolating transformer, or anything else for that matter, makes them safe under all conditions. The transformer just lets me make measurements I couldn't do without it.