LIDAR would certainly solve the problem of crashes, which is indeed a serious issue.
But I don't see how you could drive with it. It couldn't identify lane markings or exits or traffic lights or cones. And if you can do that well, you should be able to avoid hitting things.
Clearly Tesla hasn't solved that and maybe never will. But adding LIDAR wouldn't really solve the problem.
It's not LIDAR alone it's a combo. The problem of course is that Tesla/Elon is being stubborn and unwilling to put the "expensive" lidar claiming that pictures is enough to work on.
Volvo seems to be getting it right hardware-wise with it's forthcoming EX90 (electric XC90). 250 meter range LIDAR (kept clear from ice, snow and dirt by it's own heat emisssions and nozzles at the end of the windshield wipers - you can tell it's not designed in California), 5 radars, 8 cameras and 16 ultrasonic sensors.
their real problem is frame to frame consistency, due to lack of a world model.
this is what Elon talked with Lex a year (or two?) ago. (they mentioned it as how to know you are in a school zone, and remember you are in a school zone, etc)
Sounds like they're working on the world model at least in places. With the removal of the parking sensors, they've started remembering obstructions that are now out of the cameras' vision.
Personally, I'll never trust their self-driving product for anything more than lane-keeping unless they incorporate LIDAR