If the circuit is totally isolated from chassis, there is no shock hazard if B+ shorts to chassis (B- would go to the negative equivalent). But it can't be totally isolated, would be a noise nightmare. Single-ended inputs are referenced to B-, differential inputs have common-mode limits. Transformer isolation of inputs and outputs could work, feedback local or otherwise isolated. Common mode noise can only be filtered by components connected to ground, affecting the isolation. Not practical in most cases. So circuit ground must be connected to chassis ground with a low impedance. A 10 Ohm resistor, 0.1 uF capacitor and back-to-back diodes, all in parallel can do that, though a single-point direct connection may do as well.
Our AC power lines have the neutral grounded for a very good reason - lightning and similarly, power cross - the chance of a high-voltage line dropping onto a lower-voltage line. Grounding one conductor shunts most of the common-mode voltage. Some special cases do use isolated power - military vessels do, so that a ground fault won't shut everything down. Some industrial process equipment - imagine losing power to a furnace full of molten glass or aluminum or a plastic molder - much better to have time to detect the fault and have the time to shut it down properly. These would run on their own dedicated isolated transformer.
