Aperture limitations are a consequence of the design of phase detect autofocus systems and are not specific to Canon.
Phase detect autofocus in SLRs works by directing light to the AF sensor using a second mirror behind the semi-silvered main mirror. The AF sensor uses a pair of lenses to focus light from the subject onto a pair of 1-dimensional sensors, effectively lines of pixels. By measuring the offset between contrast patterns measured on each sensor the distance to the subject can be calculated. See this crude diagram (not to scale!)
The size and separation between the pair of AF sensors determines the accuracy of the AF measurement. However there is a trade off - the further apart they are, the wider the aperture must be in order to direct light to reach both sensors. In the diagram I have included an aperture stop that represents, say f/4.0 (the lens is f/2.8 wide open). With the lens stopped down to f/4.0 incoming light would be blocked from reaching the AF sensors.
Modern AF units have multiple AF points, each composed of a pair sensors at different separations and orientations. The centre point often has an extra wide separation sensor pair and thus only works at maximum accuracy at f/2.8. Often AF points have pairs of 1D pixels at 90 degrees in order to detect either horizontal or vertical detail. One pixel row will have greater separation so the AF point only works as a "cross type" sensor when using a large aperture lens, otherwise either the vertical or horizontal sensor is disabled, leaving a regular single-orientation AF point.
The sensors may work a bit past their specified aperture, as the pattern of light might overlap the sensor just enough to get a match and calculate the distance, which is why taping the pins of a teleconverter sometimes works. But in general it's not designed to do this so to prevent inaccurate or intermittent performance, Canon disable AF when the reported aperture is too small.
Canon has optimised their AF units to be very accurate with wide aperture lenses (which Canon offers at even long focal lengths, for example the 400mm f/2.8 or 600mm f/4.0), rather than to be more flexible continuing to work but with less speed and accuracy at small apertures.