Sure it does. You need more circuitry and processing power to sustain processing higher MP/sec. To sustain 12 FPS at 18 MP, you need 1Dx processing capability. More processing require larger/faster memory, processors, buses, etc. and that does take more power even when not used to to its capability.
You seem to be using the words "power" and "energy" interchangeably. Faster processing requires more power, all other things being equal, but not more energy.
No, not interchageably. A Chevy Malibu is traveling on the highway (EPA profile) next to a Corvette. Both are going the same speed. The Corvette has lower drag and is slightly lighter, yet its highway efficiency is 29 mpg compared to the Malibu's 36 mpg. Larger components (engine, transmission, etc.) required for greater performance use more power on average and more energy over the same distance.
So far, so good. But using a thermodynamic analogy isn't a good idea.
For electronics, components spec'ed for higher performance also take more power even if they're doing the same work.
In most cases, the opposite is actually true, due to thermal reasons and enabled by process technology. To have a faster device, it needs to be more efficient, not less, or it will get too hot. If it's less efficient AND doing more work, it will dissipate a lot more power, not just a little, making the thermal management more difficult.
One of the big reasons computers can get more powerful with each generation is that they consume less power per switching event. If this were not the case, we would have current generation CPUs demanding tens of kW, and burning up during POST.
Now compare options within the same generation, and your case doesn't hold water. DIGIC 5+ is used in the 70D, 5DIII, 6D and 1DX. Unless you're counting on the 7DII to sport a DIGIC 6+... Canon has a longer pro body cycle than Nikon. But what has the D4S done compared to the D4? Same MP, 1 more FPS... To get the 7D II to get the same framerate as the 1DX, which has dual DIGIC 5+ and a DIGIC 4, it'll need that same processing ability with a smaller battery. And to get more MP at that frame rate, you'll need even more processing power. So, unless Canon leap-frogs the competition in computational efficiency, I don't expect to see a large difference in Canon's processing abilities.
You're original post:
I would argue that wildlife and action photographers need it more than landscapers do. Wildlife and action often lead to focal-length-limited situations that result in heavy cropping. More pixels helps with that in a big way.
Wildlife/action applications have favored higher FPS to MP (1DX vs. 5DIII, D4 vs. D800). Nothing that you have posted has suggested that there isn't a trade between MP and frame rate, and most wildlife/action users favor higher FPS to MP.