What can you do to mitigate the danger and how dangerous is the danger? I got my first successful crop of broccoli and cauliflower this year and would like to keep it going.
This scientific study found that Plasmodiophora brassicae (the club root pathogen) was destroyed when composted in windrows at 54-73°C for 6-7 days with adequate moisture content. My compost sometimes gets that hot, when all the stars align, but I can't guarantee it's going to happen.
Since P. brassicae can survive in soil for a long time, you don't want to be spreading it around in your compost. I suppose that if your brassicas don't show any signs of disease, it may be safe to compost them. But if you do have club root, good hygiene dictates that you should dispose of the debris in a way that won't spread it around.
The advice not to plant brassicas on the same plot more than once every three years is not unusual; crop rotation is recommended for all vegetables, as nutritional needs and intake vary slightly from one vegetable group to another; therefore, growing the same group on the same plot year after year may deplete the soil of a particular nutrient and lead to unhealthy crops or, at the very least, a lower yield. In addition, it is likely to result in a build-up of the particularly wide range of pests and diseases that are specific to brassicas.
The reason why we are often advised not to compost their roots is, again, because they are susceptible to so many pests and diseases, and there may be a risk of contamination. My own plot, for instance, is contaminated with Club Root; I have overcome the problem by potting on my cabbage seedlings several times, so that they are very robust when I plant them out and can withstand the disease; I also line the planting holes with potting compost, and thanks to this approach, I've been able to keep the disease at bay, although it is still present in the soil. However, unless there are signs that your crop is diseased or has been attacked by pests, I see no reason why you shouldn't add discarded leaves and roots to your compost.