Why would you connect AC ground to an isolated DC power supply output?
Realize that this is a "logical Symbol" and has many "Analog" interpretations.

Remember that Ground only means a triangle symbol on your Logic Diagram yet we must understand this to be a 0V reference only at that physical point. System definitions are often assumed for earthing symbols or local DC only and drafting standards will vary.
In most cases, the right-most symbol denotes earth grounded.

But in other cases the middle symbol may be floating or earthed. 
So star distributed grounds are often best to avoid sharing currents, yet distributed grounds often used. (CATV, AC power and EE Lab instruments)   This leads to complications with signal integrity and immunity of the source and destination when frequent cable re-connections occur from many instruments that may be on different breakers with 3 pronged AC plugs.

It is wise you thoroughly understand the impedance of any ground at different frequency bands to see how it affects immunity and susceptibility. THe Symbols are not enough to convey these meanings.







simulate this circuit &ndash; Schematic created using CircuitLab

So the general reason is EMC as in compatibility.


THis includes immunity from interference and unintended radiation of interfering noise as well as conducted noise via AC line and signal interfaces, so there are at least 2 ports and 2 directions of compatibility to be considered.


I will only list some of the reasons.

 CM noise

THe most common reason to earth ground a floating supply is to eliminate common mode (CM) noise either from unintended SMPS noise via transformer feedthru or large step load unbalanced currents with large loop area.

Baluns 
---- (conversion between BALance and UNBalanced impedance)
Line filters use common mode chokes or Baluns to improve AC line EMC with both a differential cap and 2 CM caps to earth.  These are also useful on DC interfaces and AC signal interfaces. 

The next time you see a potential noisy interface cable, look for the plastic-coated ferrite cylinder molded around the cable (clamshell with ~no gap). e.g. Laptop charger or VGA cable.  


THOSE are CM chokes or BALUNs Important for units that are both isolated from gnd and earth grounded ( like all LCD monitors) when the signals become unbalanced and even critical for differential Ethernet signals to improve RF balanced impedance.

Another method used by some applications to reduce impact of 50/60 Hz leakage and safety concerns is to use an RF cap of 10nF or less between DC return to AC ground which acts as a low impedance of 150 ohms at 100kHz for SMPS noise or 1.5 Ohms at 10MHz.


ESD

The other reasons may be protection of an instrument with sensitive output or inputs.  Normally audio and TV interfaces may be isolated from earth ground, yet 50 ohm instruments are not.  When long 50 ohm cables with 100pF/m are charged up from dragging on a dusty counter, the voltage on the cable may be enough to blow a sensitive output or input. Although ESD protection is standard, when one end is connected to an earthed instrument, it becomes discharged by load , so that connection protects then other end. However this also makes it sensitive to ground faults, which I have experienced in a big lab with machine shop in the 70's and we had to avoid this.

This ESD subject is complex.  In most cases you can protect equipment by voltage clamps and current limiting but that may shift the local and affect something internally. Audio and TV's interfaces are generally floating with 2 pronged plugs.  Yet all lab 
 instruments are 3 pronged plugs with earth ground interfaces to reduce EMI.  This raises the HiPot insulation Field strength on primary paths such that they fail at lower potentials than floating, so immunity must be checked in this mode, but by default, never is. I found this to  a flaw in OEM test procedures for AC-DC supplies and required process improvements by OEM at my demands, when I proved this true. (OEM had moved their Mfg to Mexico and failed to recognize clearance gap process controls had slipped .eg. tilted components near chassis) 

Good and bad ESD connections.

A good connection is said to be static dissipative when 1Mohm is in series. Yet a floating cable can be charged and discharge when connected to an earthed instrument, yet when connected at one end , it safely discharges, so the other end is less likely to be impacted by a discharge. This would not be the case if both ends were floating due to stray capacitance being an effective short circuit or transient conductor to impulse ESD. If you expect ESD on long cables and want a floating supply, and have an earth ground, then a capacitor or an inductor or 1K or 1M resistor or some combination may be a better solution depending on your system immunity needs while being relatively high DC impedance to earth but low impedance at RF. 

Conclusion

It all depends on the system, but distributed earth ground is very common in external and lab equipment yet not consumer equipment and absent on portable equipment for ground leakage hand-held safety reasons.