I know that the answer is yes, I should, but outlets near the setup are not grounded (even though they look like they are) and I don’t want to have wires running though my living room.
The real question is what are potential problems ? Occasional system reboots? Permanent damage to PSU? Permanent damage to other components?
You don’t need to have wired across the room. You can put them through the wall like every other cable. If the wire tubes are not full, it isn’t very complicated. I put my Ethernet wires in the wall.