Actually there exist [book] scanners that are just that, a big sensor that images the whole page with no moving element. But they are expensive compared to getting a similar image quality with a moving-sensor1 scanner. Needs nice optics etc., also big sensor. That one uses a 35Mpixel sensor per color (105Mpixel total). Here's another one like that; this one uses a glass press, so it's more like you envisioned it. Also, a version of that that also turns pages.
1 In fact, you could have it the other away around, i.e. move the item/book as in the Google Books project, but to keep sensor costs down [to line sensor], you need to have relative movement of the sensor vs. material being imaged. Actually if you envision a book scanner that automatically turns pages, you need to have some moving elements anyway... so you might as well design the scanner around the mechanics of that movement.
In fact I've discovered a research project I didn't know about in which they flip a book really fast and just photograph it with regular cameras and then apply sophisticated deskewing/restoration algorithms. So it is possible to have your cake and eat it. I'm not sure of the image quality in this system. There's a paper about it at recent (2014) conference; in fact it got the best paper award there. They scan only at 500 dpi. To get that from the distance where the camera is at, they use ~25Mpixel (6.5Kx4.3K) camera. From this you can see the issues: to minimize optical aberrations you need to have some distance to the camera, which in turn requires increasing its resolution much more than if you scan with a sensor up close.
By the way there exist some more consumer and DIY projects of this kind; something was showcased at CES 2011; I don't know if it made it into a mass market product. Also something DIY.