As far as I know the best practice for doing high voltage measurements with an oscilloscope is either using HV differential probes or connecting the DUT to an isolation transformer while having the oscilloscope connected to AC mains with earth ground reference. I heard people say connecting oscilloscope and DUT to the same isolation transformer should be avoided.
I don't understand why (apart from maybe the devices influencing each other or someone forgetting to unplug the earth referenced USB cable.) I would consider it to be even safer, as there is no possibility to get a shock one-handed while an earthed oscilloscope could reference the isolated secondary potential to earth when measuring, which again allows to get a shock when touching. Even though the RCD would not trip when the housing of the oscilloscope gets connected to phase because of some electrical fault there is still no shock hazard as the whole system is not earth referenced (apart from leakage in the transformer coils.) If both phases are short circuited together the fuse of the isolation transformer would blow up.
Are there any obvious downsides that I have overseen or is this actually done in practice?