I first rode HONC on a mountain bike – I’m fairly sure Barrie Clarke was also on a mountain bike rather than a crosser. That would have been sometime in the late 90s.
When I last rode a few years ago on a CX bike I didn’t walk anything and after being right at the back of the field because somebody ran into me in the bunch I was overtaking people on sussers on the downhills. Sure it might not be the best on the washboard, but there’s not huge amounts of that, but it works fine on anything else. Though if it’s really dry like it was the previous time I rode I’ll be on the full-sus (lockout both ends for the road bits and lighter than most people’s hardtails, so almost as fast as the CX bike on the smooth bits).