Robotics is already on its way there. Is this program induction https://paperswithcode.com/task/program-induction ? Looks like it's headed towards ML too. I suspect you could stick ML into SAT solving and get yourself a system that worked pretty decently.
When you say "ML" you probably mean the deep neural networks approaches that are currently state of the art for machine vision etc. Deep neural network approaches have been proposed for the task of program induction but they generally lag well behind symbolic machine learning approaches.
The most coherent efforts to tackle program induction by neural networks that I am aware of is the work of Dawn Song's group at Berkeley [1] and of Joshua Tenenbaum's group at MIT. I can't find a handy link to a compilation of the latter group's work but the Dreamcoder paper in the paperswithcode search you linked to was an interesting milestone [2].
There is a lot of work on neuro-symbolic approaches to program induction, for example see the recent (two weeks ago) NeSy workshop [3], part of the first International Joint Conference on Learning and Reasoning for some new work in that burgeoning field. Statistical Relational AI combines symbolic with probabilistic learning; see the STAR-AI workshop [4] also at IJCLR.
If you're interested in recent developments on the front of program induction (again, learning programs from examples) then IJCRL is the conference to keep an eye on.
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[1] https://sunblaze-ucb.github.io/program-synthesis/index.html
[2] https://arxiv.org/abs/2006.08381
These search and sampling algorithms still play key roles in game playing AI (chess, poker, Go) and natural language generation. It is the human knowledge, specification and heuristics, part that tends to be more readily replaceable. A lot of control flow and data-structures that powered old AI approaches can be found in databases, compilers, type inference, computer algebra and even the autodiff libraries neural nets are written in.
Video game AI, constraint solving and business rules engines are probably closest to still using the full symbolic approach rather than merely extracting the control flow and structures portion.
We can therefore make a compact prediction: learned approaches replace human written computer programs (specifications, rules systems or heuristics) whenever human contribution is not valuable or is somehow harmful to robustness/generalization.
Around November 2023? I'll try to remember.