While that could be a legitimate complaint, it's not inherent to the inclusion of video tech; it's just a design error. They could easily have put some stills-oriented button there instead.
A previous poster described in detail how the design process worked, and why it is more difficult to design a product to do two different things.
It's only burning the extra juice when it's processing video. When processing stills it should be no worse than it was before. Embedded CPU's like this don't burn a lot of juice just idling.
But it's not idling, and not halted. That CPU does things other than video. They had to use a bigger CPU, which has more gates and burns more power when it is doing those other things. In some alternate design for the 1DX, there might have been a 4th processor dedicated to video that could be halted, but that isn't what we got.
The extra demands of video will push Canon to design more efficient processors and higher-capacity batteries.
I don't want a different, heavier, higher-capacity battery. I want to use my old ones. (Kudos to Canon, I can with the 1DX, but they are suspiciously silent on how many shots it wil last with an extra CPU on board, bigger than the old ones.) If there is new battery technology, I want smaller and lighter, not the same size with more capacity.
The demands of video will push canon to design faster processors, meaning better/faster in-camera JPEG (if that's your thing).
It's not, but I will admit it is for roughly the same people for whom video is. No raw video for them yet with current CPUs.
If someone with real chip-design experience wants to chime in with an explanation of how video capability limits stills IQ at the sensel level I'd love to read all about it.
Wasn't sensor heating and noise already mentioned?
Note that even the Leica M9 (a stills-only camera, if ever there was one) scores worse on DxOMark than the 1D4 for low-light, DR and color depth. Sorry folks: just not buying it.