> generated code can be verified by compiling and running it

I think this gets to the crux of the issue with LLMs for coding (and indeed 'test orientated development'). For anything beyond a most basic level of complexity (i.e. anything actually useful), code cannot be verified by compiling and running it. It can only be verified - to a point - by skilled human inspection/comprehension. That is the essence of code really, a definition of action, given by humans, to a machine for running with /a prior/ unenumerated inputs. Otherwise it is just a fancy lookup table. By definition then not all inputs and expected outputs can be tabulated, tested for, or rewarded for.