Mark Rober's video is misleading. First, he used autopilot, not FSD. Second, he sped up to 42mph and turned on autopilot a few seconds before impact[1], but he edited the Youtube video to make it look like he started autopilot a from a standstill far away from the barrier. Third, there is an alert message on his screen. It's too small to read in the video, but it could be the "autopilot will not brake" alert that happens when you put your foot on the gas.
In the water test, Rober has the Tesla driving down the center of the road, straddling the double yellow line. Autopilot will not do this, and the internal shots of the car crop out the screen. He almost certainly manually drove the car through the water and into the dummy.
One person tried to reproduce Rober's Wile E. Coyote test using FSD. FSD v12 failed to stop, but FSD v13 detected the barrier and stopped in time.[2]
Lidar would probably improve safety, but Rober's video doesn't prove anything. He decided on an outcome before he made the video.