Thank you, and I think I agree with everything you say. Yes, at steady state, as long as you don't complete a circuit, no current flows. Helicopters can be used to do live repairs on high voltage power lines, and if the pilot keeps the copter from running into anything, no one dies: https://www.youtube.com/watch?v=IgrN0fyDRsQ

Maybe what I've failed to make clear is that my real question is about the relative difference in safety of the isolated transformer as used in a "razors only" plug and the normal breaker protected outlets used in US houses. For both of them, you could stand on a dry wooden ladder and momentarily grab either wire. But the focuses on the increased safety of the isolated transformer. I'm trying to understand what exactly about this system provides for the increased safety.

From what I can tell, everything in your answer applies to both systems. It's the difference in safety between the systems that I don't feel I understand.