A plane flies and is nothing like a bird.
Most likely, the APP-E or GAME-E, given a prompt generate an application or game, will not generate C++/JavaScript/Swift/Kotlin but directly target the pixel space, running in a 60+ FPS loop a single "function" such as `nextFrame(currentState)`.
It will probably be here in the next few years: write a prompt such as "2D game like Mario but with butterflies" and receive a 2GB blob which opens a window accepting inputs and changing the pixels accordingly. Or, something more serious, a prompt like "invoicing application following the laws of France, Material Design, store the database in AWS using ". APP-E or GAME-E doesn't need to totally replace software development, just be good enough to replace in 99% of use cases.
Bugs/tests could probably be solved by some mechanism for injecting localized prompts: given an already generated binary, fine tune it accordingly to a list of other prompts.
As for deployment, it's already pretty much solved with the CI/CD solutions galore all around, not sure why you would need generative statistics for it.
What DALL-E offers is a glimpse of the next 30 years, and probably 99% of the infrastructure required to run it to its full potential is not here yet. Just as in 1992 (3 years after the HTTP proposal, but 2 years before the launch of Netscape) there were only glimpses of what a connected world would look like.