Programming languages were created because of the different problem of “its very hard to get computers to understand natural language even if you know how to express what you want in it”.
That’s not in the same spirit, and I didn’t say either that programming languages don’t solve any problem, or that there aren’t tools that do solve the problem it was suggested that programming language solve where it exists, which isn't (except maybe since the advent of LLMs) between human and computer.
Any problem with the difficulty of clearly expressing things in natural language (a real thing for which there have long been solutions between humans that are different than programming languages) was a problem that was technically unreachable at the user->machine interface because of that more fundamental problem for most of the history of computing (its arguable that LLMs are at the level where now it is potentially an issue with computers, but it took decades of having programming languages to be able to get the technical capacity to even experience the problem, it is not the problem programming languages address.)
The idea is that a programmer will work with natural language dynamically to create enough of an understanding to create a formalized specification within the programming language (eh, we technically need to include the entire ecosystem needed to run the code, but rarely is that an issue). Often it won't be perfect, but then a demo can occur where natural language can then comment on what was missed, which can then better be captured in the formal language. This continues until we get close enough that further effort to refine isn't justified.
This isn't the only reason programming languages were created, much as rarely anything has a single reason it was created. They were created as a way to get computers to do what we wanted without needing to modify the hardware, and then higher level languages were created so we can write more specification faster while losing a bit of the lowest level exactness.
Also why we have many different programming languages, as they try to fit into different levels of trade off between the different reasons for a programming language to exist. Well, one of the reasons we have many different programming languages....
I don't disagree that that is some people’s idea of the idealized process (though there are others, too.)
I disagree, though, that it is the purpose for which programming languages, as a category of tools, were invented. In fact, there were a whole bunch of tools for solving the problem of clarity of communicating expectations of sysstem behavior between humans in unconstrainted natural language invented, and that it was until fairly recently (well into the period of dominance of Agile, or at least “Agile”, methodss) the usual expectation in non-trivial programming projects that some combination of those would be used to solve that problem, and then the programmers, understanding the intent through those tools, would use programming languages to solve the problem that languages that are ideal for communicating between humans are not ideal for source languages for practical compilers or interpreters in computers.
You're conflating requirement analysis with design. The customer only needs to describe the problem — a set of constraints on what comprises a valid solution. The software engineer is then free to design and develop a particular valid solution (and show it to the customer, which will result in more feedback, which will feed back into design, and so on.)
Formalizing this split is the premise behind Domain Driven Design (DDD): you can sit with the customer and pin down a problem description (= set of design requirements) together with them, expressed in exactly the natural language the customer-as-problem-domain-expert uses, without any reference to any particular potential design's solution-space domain. You can then turn around and reuse that set of natural-language statements as the skeleton of a test suite, that "enforces" the customer's expectations upon any potential design you create.
It's a lot like an artist sitting with a customer who's commissioning them, with the artist sketching something the customer is describing; and then the artist going away to actually illustrate/paint/craft/design/etc the thing, constrained by that sketch.
