On all the DSLRs I've used, there are never any autofocus points near the edges and corners. Why is that?
Phase detect autofocus in DSLRs works by comparing patterns of light coming from each side of the lens using pairs of detectors which are separated a certain distance on the AF sensor. This distance is called the baseline, and the greater the baseline the more accurately the distance can be measured.
The need for a wide baseline and for light to travel from either side of the lens makes it impossible to have autofocus points at the very edge of the frame. The further out you go from the centre the shorter the baseline which is why the outer focus points are often less reliable.
APS-C DSLRs appear to have AF points which cover more of the frame, in reality the positions are similar to a full frame DSLR but the frame itself is smaller.
Because autofocus needs a considerable amount of light, and the lens construction gives more light getting closer to the center. Also, lenses tend to be sharper the closer you get to the center. That is why using the middle focus point and then recomposing usually gives the sharpest result.
Are you sure you'd even really want ones on the perimeter? For me, I turn off all of the auto focus squares except the middle one. Why? If I'm shooting through a tree, for example, I want to focus on my subject which may be 30 feet away. I don't want the camera to focus on a branch (off center) that is 8 feet away. I would never want focusing sensor squares around the perimeter of my lens. But that perhaps is just me.