Example fatality from https://groups.io/g/TekScopes/topic/7632418#10795 with my emphasis
What makes it so dangerous to float the scope is that it is very easy for you to come in accidental contact with the floating scope chassis and receive a very bad shock, possibly lethal. One of my first customer contacts as a Sales Engineer for Tektronix was to call on the Sylvania Lighting Center in Danvers, MA and investigate a rumor about an engineer working there that was killed while using a Tek scope. I found it it was true. During lunch, one of the engineers was working alone* in the lab on a lighting experiment that was using some 3 phase, 220 volt power. He needed to make some measurements between points none of which were at earth ground. So, he floated the scope . . . He even has the scope sitting on a scope cart with a sheet of insulation material between the bottom of the scope and the metal tray it normally sits in so the scope cart would not be "hot" with the scope. He also had a "tunnel" of plexiglas on both sides and over the top of the scope in a crude attempt to prevent anyone from accidentally touching the hot scope. The back was not covered with plexiglass in order to allow the fan to do its job and the front was not covered so the engineer could access the scope controls. This guy was WELL AWARE of the danger and took a lot of precautions to prevent shock . . . Bottom Line: He died anyway.
Anyone who teaches you that floating a scope by defeating the power cord ground lead is a very poor teacher, indeed. They simply do not know enough about making SAFE measurements to be in a position to teach electronics.
*Surely the primary warning is, if you are working on something offering unusual dangers DO NOT WORK ALONE!!
Over 40 plus years, I have only seen this done once (floating an Oscilloscope in this manner), & this was done by very senior people, very gingerly, & with great care, AND with a staff member standing by with their hand on the handle of the main circuit breaker, ready to operate it instantly if required.
This was looking for some waveform distortion problems at the output of an ac Automatic Voltage Regulator.
In a linear system, the 'scope could be set up off line to trigger correctly on a 50Hz signal.
Modern switchmode supplies means much more fiddling with the controls would be necessary, with additional hazard.
The next time I was where someone had the occasion to look at a similar signal, they bought a Tek TH720A specially because of its isolated inputs.