Found these and thought they might be interesting reading (page one of a google search for: reasons for car crashes):
From the fatal driver crashes, about half were caused by booze/drugs, speed and failing to stop. I would suspect that these days mechanical faults would probably figure someway down the list.
That being the case, the question to me would be how much would that change by extending the WoF period. From the first reference, cars older than 1984 are 3 times more likely to result in a crash with a death, so depending on the age of our fleet, it may not have a large impact, as although the cars may not be as well maintained, perhaps they are more inherently safe from a design perspective?
However, I assume the bods in the Gubbmint have done more research than I just did and the cost savings for doing less WoFs outweighs the cost of the extra crashes.