Beyond Full-HD with Canon EOS 600D? In video mode, my Canon EOS 600D can output up to a resolution of 1920 x 1080.
Of course, this resolution is a standard (full HD). But then again, even exiftool applied to an output *.MOV file tells me that the cropped image size is 2592 x 1728 (not to mention sensor size 5344 x 3516). While such video is ready to use as Full HD video out of the box, shouldn't this allow me to obtain significantly higher resolution video output (comparable to RAW for images, though still below the next bigger standard of 4K)? 

Admittedly, after editing one would certainly crop and/or scale to Full HD anyway, but who would complain about a few extra pixels in footage during editing?
Or would using this resolution cause other (technical) problems (e.g., with writing speed)?
If you do the math, you will find that a full-res video would need to process too much data per time - 22Mpixel x 30 frames x 3x14 bit color depth = 3+ GByte/second (done in my head, double-check!)

The camera sensor is probably able to provide this data, but neither the in-camera chip nor the memory card is able to process such a data stream fast enough; and the buffers would be full after 2 or 3 seconds of video. Therefore, the camera makers chose to not offer this mode.

I guess if you hack the camera software, you could it make record on that resolution for one or two seconds.