Why Aren't PC Power Supplies External?

An Anonymous Coward asks: "After years in the computer industry it just occurred to me: Why don't computers have external power supplies? The lions share of the heat and noise from a computer are generated from the power supply. Why not take it out of the case and run just the 12 and 5 volt lines into the case, leaving the heat and noise tucked down under the desk somewhere? Perhaps there is some electrical law that makes that a bad idea, but I can't think of it." One stumbling block is that a power supply brings in more than the 12V and 5V lines, it also provides the power connectors for the motherboard, internal peripherals and external fans. However, these could be provided by the case. If a standard form connector from external PS to the PC is designed, might we be able to avoid further incompatibilities like AT/ATX? It's an interesting idea for future designs, but I wonder if there are other stubling blocks out there. Thoughts?