All things being equal, the bigger the sensor, generally the better the photos and that is the law of physics and that really can't be argued. Higher dynamic range, better high ISO ability, and yes, better light gathering ability when everything is equal, ie, technology time frame (when the technology of each sensor size is at the same stage of development), aperture, equivalent focal length, shutter speeds, etc and very importantly resultant image size and viewing distances, a little gem that people don't seem to think of when discussing such matters. If you take your hypothesis to the 'nth degree, then we wouldn't need any camera larger than a cell phone and that is just plainly wrong.

Here is some light reading:
http://www.invensense.com/cn/mems/gy...hPixelSize.pdf