I'm not sure what you mean. Mechanical shutters have no upsides I'm aware of :). Astro cameras use electronic shutters.
EDIT: The dithering, or offsetting, is done by moving the telescope slightly between exposures. During exposures you want it to track the object you're photographing as accurately as possible. I imagine vibrations are a detriment even in the Pixel phone processing. It would be better if the phone could move instantly in slightly different directions and take steady raw photos in each.
Ah, I was thinking of amateur astrophotography - although these days you can just set the mechanical shutter in many consumer DSLRs to stay open too I think.
I think maybe you were considering the vibrations a source of noise for compressed sensing? For CS to work well you generally want to know the convolved noise. So a super accurate accelerometer might be able to measure random vibrations and do even better when they are present than absent. Not sure if phone accelerometers are that good.
Yes, I believe Google's team publicly says it helps add just enough random translation.
Do camera phones have mechanical shutters? I'm almost certain they don't.
On camera phones the random movements come from the users own instability when taking pictures.