Only if it helps with noise.

Anecdotally, I almost think it depends upon the buildings earth ground and if it's any good. Bad ground, then the DC side of the power supply can not float. Is this valid?

Not sure what you meant in that last sentence. A classical DC power supply uses a transformer prior to the full-wave rectification, so the DC circuit is decoupled from the "ground," which is part of the external/AC power system. While floating DC outputs have their benefits, there are some downsides, like BAD transients during power on/off through AC coupling into the DC circuit.

TTFN (ta ta for now)
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Those transients are easily tamed using an earthed inter-winding screen in the transformer. These used to be fairly commonplace on E-I transformers, but much less so on toroidal designs.

If you do leave the negative ungrounded it does make it harder to troubleshoot, sometimes it's hard to find a reference point.
With the Negative grounded you always have a reference point in any grounded metal or building steel.

I think there is also an issue with instrument amplifiers becoming saturated for example if the wiring happens to be 100 Volts DC above ground (and how do you know it's not?)

I have seen systems where they had a pair of incandescent lamps in series with the center point grounded, this keeps the system referenced to ground and it does indicate if you have a ground fault but again it can have repercussions, they escape me at the moment.

Roy

One of the repercussions is that a blown filament in one lamp immediately pulls the other rail to earth via the healthy filament. You can get significant capacitive currents flowing as the installation shifts in potential relative to earth, more than enough to upset sensitive electronics and trigger high speed optocoupler inputs. I managed to inadvertently trip 930MW of generation off the UK grid by removing an earth fault on the HV substation battery: the equipment responsible for the trip should have been resilient to the fault, but it wasn't. It was a proper brown-trouser moment in the indoor GIS substation as all five 275kV generator circuits tripped simultaneously.

Haha, that would put you off for sure, I've had a few but none as memorable as that.

One of my worse ones was a Lube oil heater controlled by a PLC reading a temperature transmitter 0 - 50C
The construction electricians powered down the 24 Volt supply overnight so the temperature transmitter told the PLC the tank was at zero
By the time we arrived in the morning the tank was almost boiling.

Ever since then I have always programmed heaters to shut off on over-temperature OR under-temperature

If u have negitive of AC not connect to earth than u can connect