Currently, side mirrors are required on cars in the US, and they can't legally be replaced by camera technologies filling a similar role. The petitioners' chief argument is that sideview mirrors add drag and decrease fuel economy. According to Automotive News, Tesla founder Elon Musk has been lobbying for laws that allow automakers to use sideview camera systems exclusively for the last two years, but claims it's nearly impossible for a single person to change the regulations.
Sideview cameras have been on concept cars for decades, but augmenting external visibility with cameras and sensors has been a growing trend in production automotive technology over the last five years or so. Nissan uses its Around View Monitor to supplement mirrors with a bird's eye composite view of the vehicle during tight maneuvers, and the LaneWatch system from Honda displays a rear-facing passenger-side view to eliminate blind spots during lane changes. Tesla's early Model X concept (pictured above) had small pods on the side with cameras mounted in them, but more recent versions have switched to conventional mirrors.
Regulations tend to move slowly within NHTSA – it delayed passing the backup camera standard five times since 2011. One day, new cars will probably drop side mirrors entirely, but that leap is still probably many years away.