They absolutely could anticipate, and arguably with more precision than people. The common occurrence of collisions when making left turns at an intersection shows that people's ability to anticipate is fallible too: people can't even anticipate that car driving towards them will continue to do so.

Self driving cars' reaction times aren't slowed by drugs, alcohol, or a Snapchat notification pulling their attention.

Current systems haven't been proven in all weather conditions and all inclement situations (ie that tesla collision with a white semi-trailer), but it's crazy to say that self-driving cars won't match or exceed human drivers in terms of safe miles driven. Waymo has already shown an 80 to 90% reduction in crashes compared to people.