It isn't strictly true that Ethernet separates data pins from power pins. Because the data transmission is differential, you can send power over the same cable. (The audio world has been using phantom power for years over XLR cables -- its not a new technique.)

eg, Gigabit Ethernet has no unused pins, and can still support PoE.

That's true, I should rephrase it as "Ethernet is not designed to carry any significant current. On any pins. At all. So don't connect your twisted-pair to your two-prong."