I find it unlikely that consumers are as safety conscious as you imagine them to be. Think about how many people currently text or do other things to distract themselves while driving. They willingly choose less safety in order to be able to do something else while in transit. Pushing this behavior to its natural conclusion is what will allow self driving cars to be accepted even if they are 10% less safe than normal drivers.
People text while driving because they think they are better at doing two things at once than they actually are. For the same reason, they will expect that they can out-perform a robot unless those robots are so overwhelmingly safe that conclusion can't be rationalized. No consumer will be thinking about the big picture.
