The entire residential electrical grid in the USA uses 240v, split phase. One hot wire at 120v, one neutral at 0v, and one hot at -120v, out of phase with the other hot. Very rare to have anything else. It’s just that inside the building, the outlets/lights are connected to one side of the split phase connection or the other, giving you only 120v to work with. But then we have special outlets for electric clothes dryers, EV chargers, etc, which give you both hot connections in a single receptacle, for 240v.

As far as I’m aware (and as shown by a limited amount of testing that I’ve done myself), any modern PC PSU (with active PFC) is totally fine running on split-phase power: you just use both hots, giving you 240v across them, and the ground. The neutral line is unnecessary.

If you installed a European outlet in a US home then it would be using the same split phase configuration that a NEMA 14-30 does. But many appliances will work just fine, so long as they can handle 60 Hz and don't actually require a distinct neutral and ground for safety reasons. Likewise NEMA 10-30, the predecessor to NEMA 14-30 which is still found in older homes, does not have a ground pin.

Yes, but a standard household wall socket in the US supplies 120V @ 15A, for a max continuous power of 1.4 kW or so. So typical power supplies are only designed to draw up to that much power, or less.

If someone made a PC power supply designed to plug into a NEMA 14-50 you could run a lot of GPUs! And generate a lot of heat!

You can replace the receptacles with ones meant for 240VAC at the same time you modify the wiring. Then it should be okay. Replacing the NEMA 5-15 receptacles with NEMA 6-15 receptacles would work.

This explains why a number of people in Europe seem to love the idea of having triple phase to DC on board chargers on electric cars, even though it makes more sense to have those at the charging points.

That said, a typical socket likely varies more in the U.S. than in Europe since anything that is high draw in the U.S. gets 240VAC while Europe's 220VAC likely suffices for that. I actually have experimented with running some of my computers off 240VAC. It was actually better than 120VAC since the AC to DC conversion is more efficient when stepping down from 240VAC. Sadly, 240VAC UPS units are pricy, so I terminated that in favor of 120VAC until I find a deal on a 240VAC UPS unit.