Andrew- Since use of carts in the CGA run State far predates the US SupCt decision involving Casey Martin, I doubt the reason is legal (and, being an attorney, I have some expertise in this area).
Its just that its been traditionally done, and the additional factor (perhaps most important) the necessity to obtain courses, north and south, for qualifying events-
The Conditions of Competition should always be the same for the qualifying rounds as they exist for the finals. Hence if you allow electronic yardage devices in the qualifiers, you allow them in the finals (one of the reasons we allowed them, contra USGA policy for their national events) is because many of the courses used for our qualifiers had GPS systems on their carts that were difficult to turn off)--
By the same token, many of the courses we use for qualifiers would not be available if we barred the potential revenue they receive from cart traffic. We don't have quite the pull the USGA does in getting qualifying sites for National Championships (which in Calif are largely private courses for USGA qualifying, whereas we need some public access courses for CGA and NCGA and SCGA qualifying events)--
To keep the entry fees reasonable and attempt to secure the best courses possible you have to extend to the courses that hold these events the revenue stream possibilty (for most state qualifiers we do pay a per head green fee--which is often not true for the USGA events we conduct, which have the "no cart" restriction)--
We encourage walking in the finals, but if we permit it in the qualifiers, we are bound to allow it in the finals.
So I think it gets back to bottom line dollars, not legal issues.
More seriously, the CGA does appreciate the feed back you and other players provide re the event, its format and its venues. We do listen to the players since they are the key to these events.