>> I am not belittling the work going in this space, and I’m sure for highly constrained and narrow use cases a lot can be done even now.
No. Program synthesis approaches work very well for a broad array of problems, not for "highly constrained and narrow use cases"- that is a misconception of the kind that results from lack of familiarity with modern program synthesis.
Here's a good recent review of the field:
https://www.microsoft.com/en-us/research/wp-content/uploads/...
Sumit Gulwani, that I mentioned in my previous comment, is an author. To clarify, I'm not in any way affiliated with him or his collaborators. I'm actually from a rival camp, if you will, but the paper I link to is a very good summary of the state of the art. It should help you if you wish to understand where program synthesis is at.
>> I said program synthesis good enough to replace programmers requires AGI. Program synthesis based off of informal specifications in natural language.
Program synthesis from natural language is hard to make work because it's difficult to translate natural language specifications to specifications that a program synthesiser can use. But that is a limitation of current natural language analysis, specifically natural language understanding, approaches - not a limitation of program syhtesis approaches.
I think you equate formal specifications, or specification by example, with "narrow use cases". There's no connection between the two.