But..This ignores a few things. First that, like you said, it is the same flow and pressure. This means that across the 12" the same amount of water is hitting the surface at the same pressure. Well, almost anyway. The reality is because of the wider fan pattern the distance to the carpet increases as the distance from center does which lessens impact slightly.
Try this. Fill a 5 gallon homer bucket with coffee and suspend it 10 ft or so in the air. Connect it to the supply side of your pressure washer. Now find a dirty piece of concrete and hold the lance about 6 inches from the surface and cycle through the jet angles. Two things you will notice is that A) the narrow jets angle provides more "impact" because the same amount of water is hitting a narrow area and B) the widest jet will tend to show banding where the center cleans better.
Now back to the wand jets. Since we are splitting the flow across more jets you will lose some of the increased impact (A) but gain a more even impact across the interface (B). The net resulting difference in force being negligible imo. Again, the same amount of water at the same psi is being delivered. The narrow jet patterns making up any difference in impact that may be "lost" due to reduced flow to any given jet and providing more even delivery.
More jets can also be closer to the carpet allowing for less impact loss as well as a lower profile on the wand itself.
I let it go last time this demo was posted