Here is my understanding of the 4 pin 12V connector.
The 20 pin ATX connector has one pin on which 12 volts comes in. Meanwhile it has 4wires for 5V, and many ground wires. The electrical reason for more wires is
1) heavy currents cause less of a voltage drop with more and bigger wires. 1a) The larger surface of more wires also represents a lower source impededance at high frequencies. But this is DC you say? The CPU and other components switch at high frequencies and draw current in corresponding pulses up into the gigahertz. In order for the DC voltage to stay absolutely constant, the source impedance would have to be zero. An impossibility. So AC appears on the DC line, which is very undesirable. To minimize this you want the AC resistance (impedance) to be as low as possible. More wires is the easiest way to do it.
2) The connector pins are rated for a certain current. With more connector pins, a higher current can be sustained without the contacts overheating, and possibly melting and burning. I saw one site where a reviewer had a picture of the ATX connector of the mobo as he received it for testing. One pin was scortched and the white plastic brown. A connector in that condition is unrealiable, and even dangereous, even though the mobo performed flawlessly.
So newer mobos are possibly using higher currents from 12V than was anticipated when the 20 pin ATX connector was engineered. They do that to take some of the load off 5V, I imagine. With switching regulators, you can use any starting voltage. Intel in particular puts out recommendations in its tech sheets about how to design the power regulators and what sort of connectors should be on the mobo. Taiwan mobo makers take that seriously and go along. Their bread is buttered with Intel. Taiwan makers try to make AMD and Intel mobos as similar as possible, for simplicity of engineering and lower cost.
It is possible to design power regulators to turn on extra circuit when there is current through this other connector, but I don't think that is what they generally do. If a mobo works at all with the 4 pin connector unplugged, it appears that the ONLY thing the 4 pin 12V connector does is provide extra wires. The net result is that people wonder why they even put the connector on there. Suffice it to say that things like connectors and wires can sustain themselves well beyond what they are rated for. That is intentional, and a good thing. Still, the better way is to run things within their ratings. So is the mobo and the 20 pin ATX connector being run with its design parameters or not? AMD engineers so far think it is OK without the 4 pin connector. AMD engineers also think their retail HSF keeps their CPU cool enough, and it does of course. Enthusiasts don't care to settle for that.
I'm going to tag this on: Reviewers seem to like the ATX power connector in a position that is convenient. But there are things more critical for a multiple gigahertz computer, and I would prefer that mobo designers not compromise electrical performance to satisfy this predeliction of reviewers. Putting the ATX connector close to the CPU, and the regulators right next to that, would normally be consider the ideal place electrically. It's not some obscure principle known only by reading esoteric electrical engineering journals.