That again.
No it's not an absolute requirement that there is a ground connection to the output of an isolation
transformer.
In fact european standards absolutely demand that there not be one.
The isolation transformer makes a class 2 (double insulated) device out of a class 1 (earthed
chassis)
device.
All exposed metal parts of the powered device end up connected together, but floating.
You may not connect more than one appliance to an isolation transformer (each needs a separate
transformer).
You may not connect any other external sources to devices powered by an isolation transformer.
I agree there are many cases in which an earth connection on the output is better.
Especially if you ignore the rules about external power sources such as is often done when floating
scopes.
Chapter and verse about isolation transformer configurations here
And here, towards the end
The general conclusion is that many configurations are allowed provided that they do not compromise
safety. One of which is to carry the ground from primary to secondary.
Craig