"Foolish" is a strong word, though it may apply on some courses. Lack of foot retention off-road can be dangerous, as you could have a foot bounced off a pedal with unpleasant results. Toe clips keep your feet on the pedals, but then you have the new danger of not being able to disengage from the pedals immediately when needed.

In short, I suppose you could race cyclocross on flat pedals, but I wouldn't recommend it.