Imagine if the graphics card's PCB component legs, as well as the soldering, accidentally touches the metal case if something or someone abruptly moves the PC case while it's turned on... With the case directly grounded/going to neutral or, even worse, plugged in US power outlets with reversed pins (so 110 volts now runs through the metal case, ready to find circuit with the secondary voltages running through the graphics card's PBC trails).
Best case scenario is the user's fingers discharging accumulated amounts of static energy when they touch the case while also touching some card's circuitry.
ATX power supplies are literally some of the safest power supplies to exist, and a GFCI breaker would prevent this scenario from even happening IMO lol
Where exactly do you think the middle pin from power outlet goes?
If not to ground the metallic husk, then the third pin is useless there.
It's there with a purpose: it's meant to ground, generally (present at the best of electrical house infrastructures) going all the way to a buried copper rod that creates a short circuit with the ground present when someone is touching the metallic husk. Also, in US, IIRC (I'm from Brazil so I don't know the US electric system so well, although old Brazilian outlets are inspired by US outlets) they have GFCI (Ground fault circuit interrupter): if GFCI detects flowing energy at the ground, the outlet shuts off, protecting people from electrical shock.
However, on many houses, neither GFCI nor proper ground is present. Some houses (it's common in Brazil with older outlets inspired by the US outlet) route ground wire to the "neutral", be it on the outlet, be it on a DIY extension cord. The latter will allow for neutral to be plugged into phase, so ground will be phase as well. From there, I guess I don't need to detail what happens if someone touches a phased ground. Zap!
In Brazil we have a different kind of outlet, one with a specific shape (inspired by the Swiss power outlet) that won't let us plug reversely. With these outlets, phase goes to phase, ground to ground and neutral to neutral. Old houses still have the US-based outlet, tho.
Modern US plugs have a wide blade for "neutral" or "return path" and a narrow blade for "live" or "hot" (plus the round ground pin). In my part of the US, we only have GFCI near water (restrooms and kitchen) but always proper circuit breakers and ground to water pipes where the mains AC enters. There still exist many 2-prong appliances, but those will never have the case connected electrically!
If you don't have a proper earth ground, then tying anything together is bad news. You could have one appliance shorting out and damaging others on the same circuit, or burning your wires in the wall. Regarding the PC switch-mode supply, AC in goes to a transformer which doesn't care if hot and neutral are swapped.
Sorry if I sounded like a jerk. I've been working on PCs and appliances for decades and only once ever had an energized case; not a PC. Touching two machines each plugged into a seperate circuit, got a metallic taste in my mouth, pulled out the meter and measured ~80VAC! Verified my vending machine and outlet were wired correctly and recommended getting their popcorn machine and outlet checked out.
3-prong plugs (which computers use) have never been possible to insert upside down, and 2-prong plugs have been required to be polarized (one blade longer than the other, so impossible to insert upside down) since 1962. Aside from this, all voltage rails in a computer are electrically isolated from both sides of the mains. Most connect their 0V rail to the ground pin of the wall outlet, but there is no path from the AC lines to the DC. Touching a PC case has a 0% chance of electrocuting you.
Regarding the graphics card, one side is covered by the fan shroud and the other by the backplate. No part of the bare PCB is exposed to the chassis. Even if it was, there is more than enough clearance to keep anything from shorting out, and if there isn't, a piece of foam is all it takes to fix that.