Interesting article from NYT that explains some of the reasoning:
"At the beginning, Autopilot used cameras, radar and sound-wave sensors. But Mr. Musk told engineers that the system should eventually be able to drive autonomously from door to door — and it should do so solely with cameras, according to three people who worked on the project.
They said the Autopilot team continued to develop the system using radar and even planned to expand the number of radar sensors on each car, as well as exploring lidar — “light detection and ranging” devices that measure distances using laser pulses.
But Mr. Musk insisted that his two-eyes metaphor was the way forward and questioned whether radar was ultimately worth the headache and expense of buying and integrating radar technology from third parties, four people who worked on the Autopilot team said.
Over time, the company and the team moved closer to his way of thinking, placing more emphasis on camera technology, these people said.
Other companies developing driver-assistance systems and fully autonomous cars thought cameras were not enough. Google, for example, outfitted its self-driving test cars with expensive lidar devices as big as buckets mounted on the roof.
Cameras, by contrast, were cheap and small, which made them appealing to Tesla for its sleek cars. Radar, which uses radio waves and has been around for decades, was cheaper than lidar, a less common technology. But according to three people who worked on the project, some engineers backed Mr. Musk’s cameras-only approach, arguing that radar was not always accurate and that it was difficult to reconcile radar data with information from cameras."