You can also use EVGA's power boost. It does the same thing as powered risers: stabilizes the PCI-E bus by providing it more current. Powered risers power the motherboard, not the card.
A full sized card, even on a 1x slot, is going to want to draw 75w. Yes, they are "rated" for 25w but can use as much as 75. All the power pins are near the front of the card so there's nothing stopping it from doing so--the card doesn't care if it's in a 1x or 16x slot. This puts more stress on the motherboard, which may or may not stand up to the load. Use a power boost or powered risers for peace of mind, at least. Nobody likes the smell of burning plastic.
That's completely wrong.
The cards draw about 25-50 watts on the pcie slot. They draw from 150-300w on the pcie power connectors. I've tested this many times with a variety of cards. The powered risers power the CARD, they run the fans, and the communications side of the gpu. I haven't seen a card draw more than 45 watts at full power through the power connector on the riser cards. Power boost has nothing to do with what the capabilities of the amount of copper in a motherboard trace can handle are. Six cards trying to draw 40W each is 240 watts, through a connection probably designed to provide 100-150. That's why people have problems, and that's why the powered risers are so nice.
PCIE specs dictate that a full sized graphics card pull up to 75w from the slot. Whether they actually do, I don't know. But it's there in black and white. Do graphics cards on a riser know whether they're plugged into 16x or 1x? If not they may try to pull that from the slot. Your findings indicate that they don't, which is good.
Electricity follows the path of least resistance, so once you plug a powered riser (or power boost) into the pcie slot it simply becomes part of the circuit. In that sense it's providing power to the pcie bus which in turn powers the card, not directly powering the card. That's why the power boost and powered risers accomplish the same task, even the the power boost is a standalone product that uses an empty pcie slot.