On a CCD sensor, the mechanical shutter has to be closed to read the image out of the sensor accurately. If you could hold the mechanical shutter open, the images produced wouldn't be as high a quality. CCD sensors produce video this way, but a very bright light, like the sun, will mess up the entire sensor column, producing purple vertical lines.
The amount of time the CCD sensor is collecting light is controlled electronically, and by CHDK, so very fast shutter speeds are possible.
CMOS sensors collect light all the time. They can be reset and read out instantaneously, so you reset it, wait the desired shutter time, and read it out. However, you can't read the entire sensor all at once, so the maximum shutter speed is determined by how fast you can read the entire sensor. It takes longer to read high megapixel sensors than low megapixel ones.
The other problem with CMOS electronic shutters is that the camera doesn't expose the entire sensor at the same time, called the "rolling shutter" effect. It's a big problem with flash photos, so that requires a mechanical shutter to work right.
It should be possible to use only the electronic shutter on CMOS cameras and disable the mechanical one. Taking video is done this way (with rolling shutter artifacts visible sometimes). I think the Nikon 1 V1 camera has the option to turn the mechanical shutter off.
On my sx-260 cmos camera, the fastest Canon shutter speed is 1/2000, which I assume is done by the mechanical shutter. I've experimented with going faster with CHDK, and the maximum it will do is 1/3200 (2/3 ev faster).
The mirror in an SLR is just there to be able to see exactly what you're shooting. It pivots out of the way before the mechanical shutter (which is also the aperture control iris) takes over. Point and shoot cameras don't usually have mirrors, since they use electronic viewfinders. The "silent timelapse" feature of Magic Lantern sounds like it may be holding the mirror out of the way like you want.
Thanks for bringing up an interesting topic. If someone knows more about the various shutters, please add your comments.
