To play devil's advocate - somehow I drove myself to work today, and the hardware I'm running is just two moderate resolution limited field of view cameras. Not an expert, but from first principles it should be possible to pilot a self-driving car with cameras only, given enough processing power and a smart enough agent. Maybe those last two aren't there in 2018 though.
This sounds like a fallacy (not sure which one). Just because you can do it does not mean a machine can. There are things that babies can do that machines can't (in 2018).
I'm not saying it won't be possible at some future date after some hypothetical breakthroughs, but we are far from it presently.
Lidar range is more than double visual range, in practice.
When figuring out collision avoidance paths for an object you actually end up approximating some np hard problems to find a path that won't have collisions and won't be too "careful".
This ends up being fairly computationally intensive, and adding the extra time significantly improves your planning. Doubling compute time tends to beat doubling your training dataset in terms of system quality, at this scale.
Extra time also turns a number of situations from "guaranteed kill" to "we can avoid the accident", because the car is traveling really fast and those extra seconds can be used to brake, find a new path, etc.
In visibility impaired situations, lidar and vision have different constraints and ways they fail, and the intersection of the two can significantly improve scene understanding ( see waymo's snow demo ).
In a lot of cases, path planning can be dramatically improved by having maps. If you're going into a curve and know the shape of the road, you can preload that and spend your time on more important tasks like object detection and path planning.
Etc etc etc.
This is absolutely not a domain for intuition and thought experiments. The pragmatics of the industry are highly intricate and responsive to constraints that are only visible if you've worked on this stuff.
There is something in the middle between your pairs of eyes and your decision making that makes you understand what is actually going on around you: perception/cognition.
If this was so simple as you put it (and in particular just by throwing algorithms and processing power at it), several problems would be trivial by now and we all already would have our personal digital assistants... I mean the real deal.
Well knowing I sound like "dismissive grampa" right now, and yes, we have come far and it is impressive, but I sometimes feel like us nerds/hackers/software guys tend to considerably underestimate most problems, and as consequence the intelligence and efforts of those that came before us.
Smart enough is also pretty hard, especially for edge cases. For example, imagine driving on a highway and there's a discarded grocery bag flying around. Based on the flying pattern, it's pretty easy for you to identify such an object if you've seen one before. For a deep neural network, if it hasn't seen enough examples of such objects, it'll fail to classify it properly. What will a self driving car do if it sees an unknown object in front of it while driving at highway speeds?