If you gave someone in 1994 the GPT-3 code and dataset, it would be impossible for them to regress and very difficult to run even if we regressed it for them. AI algorithms may not be limited by "what we tell them" but they ARE limited by the hardware we run them on.
NN models do converge to something (both in the sense of regressions converging, but also in the sense that adding more nodes eventually stops improving performance at a given task.) I suspect but cannot prove that in most cases what it converges to could be expressed more concisely and efficiently as something other than a NN. (I.e. that NNs can approximate any function does not imply they can do so efficiently)
So at the end of the day, the programmer needs to understand the algorithm well enough to know if a NN-based implementation of it would achieve sufficient performance on available hardware. If the answer is no, then the programmer still has to come up with something alone.