Somehow I doubt this problem is as simple as "add a LIDAR" considering there's probably at least one smart person at Tesla who has thought of that idea. Sure you might be right, but my impression is that the 1 in a million cases will still exist.
Adding LIDAR would make the millions of cars on the road a liability. You'd have to make those people whole and basically recall the cars. If you can 'make it work' with cameras, you save millions.