The DSLR is bigger than the SLR due to the battery, memory cards, a whole bunch of electronics and motors inside the body. Plus every body wants a hand grip for the DSLR.Look at compact digital cameras, they also have a ton of electronics in them. I can imagine the "stuff" would easily sit in place of where the film rolls would otherwise go. The mechanics between a SLR and DSLR I think would be near enough the same. I do think the LCD on the back is one of the biggest consumers of volume, so removing that would allow bodies to get much smaller. That also removes the need for the power so batteries could be smaller too.
I don't really need the back LCD, but it will never go away in a mainstream camera. It is one of the features that attracted the masses to digital cameras, they can tell if they actually captured a photo, and many carry their cameras with them to use as a display gallery to show photos they took.
The big user of space is the mirror. EF Lenses are designed with a focus distance to account for a FF mirror. Remove the mirror, design new lenses with a short distance to the sensor, and a huge reduction in size occurs. Thats why the 35mm film point and shoot cameras were much smaller.
Once you remove the mirror and design a new set of lenses, the size of the sensor doesn't have much effect, its the lens design.
Canon could design a new set of lenses with short back focus distance that covered full frame, and make a small FF point and shoot, or interchangable lens camera. So could the others, but Canon does have a jump in FF technology. Fast and accurate autofocus is the hurdle.