LIDAR probably would help to make Phantom Brakes happen less often, simply because there would be another info source for "is there REALLY an object that is dangerous to me?".
Those who say that FSD is "pretty good" are living in a fantasy world. There is hard data on miles between critical disengagements (which really should be called "if the driver doesn't respond within a fraction of a second, people will die"), and depending on region, model, weather etc it's between 13 and 115 miles right now.
Over here in Germany there are statistics that a human driver will have the equivalent every 155,000 miles.
"Pretty good" just doesn't cut it when it's about the risk of killing people.
My Model 3 right now detects about 60-70% of school children crossing the road (keep in mind roads in Germany are narrow, and humans including kids are using the roads, too). 30%-40% of those I would kill every morning on my way to the office.
And the thing is: 70% isn't enough for this, 80% isn't, 90% isn't, 99% isn't, and 99,999% isn't.
Side note: People constantly claim that Waymo is autonomous. It's as autonomous as a tram. They only work because it the cities they operate every single road they use have been mapped by hand and is constantly updated. Send a Waymo into my city over here, and will also kill a couple of kids per day. Years ahead of Tesla? Yes. Good enough? Hell no.
It probably is, actually (and sadly).
Looking around at the percentage of drivers around me on the road with their face looking at a phone, while moving, is probably in excess of 5%. These people won't see the kids crossing the road, either.
The problem isn't that the sensors need to be added now, the problem is that without the sensors the cars are half blind and are more likely to make bad decisions and refusing to add them at all shows bad judgement.
Rain, snow, mist, fog, darkness -- these are things cameras are very bad at seeing through. Is that thing in front of us solid? Without extensive training on that particular type of object, the AI with the camera has to guess. I'm sure these aren't the best examples -- I am not an expert in LiDAR. But I do have experience with computer vision with camera systems, and they are woefully insufficient for life and death decision making systems when they haven't been trained on the exact specific scenarios they will encounter.