BK 1653 Isolated variac, when NOT to use?

[county]

I have a BK 1653 isolated autotransformer, as well as a standard non-isolated autotransformer.
I use these devices for repairs of analog electronics on a daily basis, but I usually the non isolated variac.
Is there ever a situation when I WOULDN'T want to isolate the DUT? 
I know WHEN to use an isolated supply, but I'm not sure when I DON'T want to use an isolated supply.
Any thoughts?

[AG6QR]

You don't want to use an isolated supply if you want the safety of having a working ground fault interrupter (known as RCD in some parts of the world, GFCI in others).

If there is a single fault between some part of the DUT and an earth ground, with a GFCI, power will be cut.  With an isolation transformer (whether or not a GFCI is feeding the isolation transformer), power will not be cut.  Such single fault won't immediately result in a person receiving a shock, but it means there is a possibility that a person could be shocked if he touches ground while touching a portion of the DUT that is at a different potential than the grounded point of the DUT.

There are times when isolation can be a good, or at least not bad, thing.  But not always.  If isolation were always a great thing, our electrical codes would require isolation of all household wiring.  Codes wouldn't require that the neutral be bonded to ground at the service entrance.  Usually, I'd rather stick with the electrical codes and have the safety of neutral bonded to ground, combined with a good GFCI. 

But when you need to do something unusual like use a ground-referenced scope to probe a device in an unusual way it can be reasonable to use an isolation transformer, with caution.