Aw come on, I thought the lasers versus watermelons demo was a lot of fun, and if that isn't mad science, I don't know what is

Theoretically, yes. A human would be smart enough not to drive right into a painted wall, using only their eyeballs combined with their intelligence and sense of self-preservation. A smart enough vision system should be able to do the same.

Using something like LIDAR to directly sense obstacles would a lot more practical and reliable. LIDAR certainly has enough distance (airplanes use it too), though I don't know about the systems Tesla used specifically.

If for some bizarre reason you would want to stick to cameras only, you could use 2 cameras and calculate the distance to various points based on the difference between the images. Thats called stereoscopy and is precisely what gives our brains depth perception. The issue is that this process is expensive computationally so I'd guess that it would be cheaper to go back to lidar.

Can this be solved with just cameras

Theoretically yes, but in reality, not with current technology.

but thought that would only be effective short range

LIDAR actually has quite a long range. You can look up some of the images LIDAR creates, they're pretty comprehensive.