As charges get shifted down a column they move from sensor to sensor, and they will gather additional electrons from illuminated sensors. The added electrons act to smear the image, thus the need for a shutter. By incorporating the sensors right in the shift register, a full-frame CCD requires no extra space for shift registers. Thus, these devices work well in applications that require high-resolution images because sensors can cover almost all of the CCD's surface with no gaps between sensors. Almost all the light that hits the full-frame CCD gets converted to electrons.
Speed can suffer, though, particularly in large arrays.
Keep in mind that the CCD must shift out all the video information before it can start to acquire a new image. One array uses its MOS capacitors to gather light. The second array, which is not light sensitive, provides memory cells for the image information. After the array acquires an image, circuitry quickly shifts the charge packets for the entire image, or frame, into the memory. The memory can then put out the image information using shift registers as described for a full-frame device.