Float Function generator
Because you can touch the BNC connector (outer shield), it is often treated in safety
testing as part of the case.   So, it is possible for a test protocol
to make a 30 ampere test current run from that BNC to the AC ground
pin on the power cord.   

It is easier to justify grounding the shield, or using a CM choke on the signal connector 
and wiring the BNC shield through that to the case.   Or, one can
operate a function generator on battery power, with the AC cord
and its ground wire completely detached.

To actually float the BNC shield as you want, might only meet safety
standards with a class 2 power supply, or battery power.