The task of racing is very different then the task of driving. It requires aggression, not caution. Current driverless cars are all about not crashing, and that is a very different problem.
It's really different. For example, there needs to be a yellow flag mode where cars hold their relative place. When there is an accident with debris on the track, how do you clear the track? Do all the cars stop?
Can the navigation algorithms execute responsively enough at track speeds? Many of the current automomous vehicles use 3D scanners. Can those keep up at high speeds? How does the common vehicle encompass all the different sensors that various competitors want to use?
Look at the results of the DARPA Grand Challenges. The cross desert race was won by the team that manually added a large number of way points, in some sense defeating the intent of the challenge. The more recent robot challenge showed that humanoid robots are not ready for very much besides walking and cannot traverse uneven terrain. Why should race cars be any different?
Still, I think it would be an entertaining first lap where everything goes to hell and the track is strewn with really expensive gear. You could make book on how many cars make it past the first turn. Zero would be a good bet.