There's nothing to keep manufacturers from creating a UPS in the shape of an ATX power supply.  I don't know how much of the ATX internals are devoted to the various rail circuitry, but if it's minimal enough, then why not do this.  The rest of the PSU hardware could exist as a block like those that are on the power cords of every laptop out there.

Just don't expect the PC to run for hours when the power comes down, but I can't see why it isn't doable.