IMO Tesla does not have the hardware on the Model 3 to do full self-driving.
I believe that stereopsis (multiple cameras using parallax to solve for per-pixel depth) is necessary to get a practical, well-functioning self driving system working. LIDAR is just too expensive and not good enough, but stereopsis is extremely flexible and can have extremely high angular resolution.
Combine naive stereopsis with temporally-coherent sensor fusion (e.g. a well-designed Kalman filter), and I think you could have very robust ranging. Humans are already very good at this with two narrowly spaced eyes (stereopsis to 1/4 mile range is not unreasonable for a person)-- but a car is not limited to a 1.5 inch stereo baseline; it could have a stereo cameras on opposite sides of the windshield. That would hugely increase the depth sensitivity, even at moderate resolution-- parallax can be detected well below the Nyquist limit (since Nyquist cuts off frequency, but does not destroy phase).
Tesla is totally failing at even the basic level of environment awareness (c.f. cars which have been driving into exit dividers), which is what I consider to be the easy part of self-driving (the hard part is getting the machine to participate in a nonverbal social environment, which is what the roadway is). Rumor has it that Teslas can't detect obstacles far enough ahead to avoid them at more than 30mph-- absolutely abysmal, if true.
If it were me, I would put cameras on the Tesla windshield in this pattern:
xXoO OoXx
Where x and o are long-range and wide-field cameras, and caps and lowercase are dynamically exposure-adjusted to capture both brights and darks. Each pair has the largest possible parallax baseline. And I would do a big, fat sensor fusion on all eight of them to get a high-res, depth-augmented HDR map of the surroundings. No fancy, expensive sensors. Just a large number of cheap cameras and sophisticated software. Maybe do some tricks with cycling 'attention' or multi-res hierarchies to keep the computation load down and realtime.
Tesla has only three cameras with different FOVs and a very narrow baseline-- I doubt they are doing stereopsis. And I don't think they can do the job without it.