I don't think it is quite that simple of a solution. I think there are a few contributing factors that possibly answer your question:
Cost. Elon's goal was to rapidly scale an affordable autonomous driving solution. When the decision was made, LIDAR was still a relatively expensive sensor that significantly cut into that goal. If it's expensive, it's not really scalable. The facts have now changed a bit, but Elon is committed for better or worse.
Neural net training. It's a relatively straightforward process to train a neural net by having it watch a huge amount of video of good drivers and learn from those examples. The data set for driving with LIDAR is a bit "fuzzier." The data set isn't nearly as big and it's a bit more abstract on how one could use it to train a neural net.
There were reports that Tesla was having difficulty with its algorithm based FSD model with respect to prioritizing information between radar and visual sensors. So they punted and went visual only.
LIDAR is most effective in a very well mapped environment where it can compare what its seeing to a recorded baseline. Musk didn't want that restriction. He wanted to build a solution that was free from the pre-mapping requirement.
I don't think the final jury is in on his decision.