It would be possible to use cameras instead of ultrasound, but that would require mounting a lot more cameras in the dead zones as you said. One of the coolest things I've seen was on a BYD, which has cameras mounted pointing downwards all around. It then creates a fake birdseye view when you are parking, or close to an obstacle. It looked really convincing, as if there was a drone above the car.
I mean damn that looks legit. I'd like to see how it performs at night when you're trying to park in some unlit parking lot, but otherwise that's a pretty amazing projection right there. The dream of driving in 3rd person view is finally here.
I had a Lexus ES 350 loaner the last time my (22 year old) Lexus was in the shop- it had the same feature you describe in the BYD. There was obviously some stretching/warping trickery being done to create the birds-eye image, but it was really impressive regardless.