How can I photograph book pages so they look more like a scanner output?

You can certainly get much better results than you're experiencing now, but it's going to take a bit of fiddling around to do it.

The "real world" has a lot bigger range of light-to-dark than typical ink on paper. The paper isn't nearly as white as you think it is, and the ink reflects a lot more light than you probably think it does. In pictures of the "real world", the brightest brights are both lighter in color and are in brighter light, while the darkest darks are both darker in color and in shadow. By comparison, there is only the difference in reflectivity between the white of the paper and the black of the ink in a "process" picture.

Real-world images tend to average to middle tones too. Your camera is designed to look at the scene before it, measure the light and adjust things so that the middle tones in the image are rendered with a middle-grey brightness. (The algorithm is actually a little more complicated, in that the camera can judge an overall light or dark bias and can, to a degree, recognize some types of scenes and adjust for the "usual" exposure for what it's recording.) So you are shooting what is, in effect, a low-contrast scene with more white than the camera is expecting (the ink coverage for text is usually only about 5%, and the camera is expecting the scene to have an average reflectance of about 18%).

To get the right exposure, you're going to have to use the exposure compensation to increase the exposure a bit, making the whites whiter. Increasing the light levels will help a lot as well since the reflectance of the paper is (usually) higher than that of the ink, so you'll get a better starting contrast. But you'll probably still need to increase the contrast over a "flat" capture.

Your camera may have a scene setting for that that's aggressive enough to do the job, but the chances are that you'll need to set the white and black levels for the picture in post-processing.

As for why it's easy on a scanner, well, the scanner knows how much light it's throwing at the page (it doesn't have to rely on measuring the reflected light) and it also "knows" that it's going to be dealing with a smaller range of tones (nothing can be brighter than the whitest paper, nothing can be darker than the blackest ink, and shadows are anomalies that only happen when you scan solid 3D objects), so it will bump up the contrast to suit.