The parallel is real, but in math the "cash value" of the results often won't appear for years, if at all, and so the teaching and "intellectual fortification" is the primary point of the whole enterprise (at least, a major part of it).
In contrast, the value of a program is typically just the "black box" service it provides. Indeed, the program itself has always been opaque to most business stakeholders. Before, they paid human programmers and got back a program they didn't understand but could use; now, they pay an LLM provider and get back a program they don't understand but can use. In the pre-LLM era, the economic value of "understanding" and "shared knowledge" about the programs themselves was only that it made maintenance and changes cheaper. It never had intrinsic value, except as intellectual satisfaction to programmers (I was... am... one of those who found that value).
Only if you assume that all software works the way that product managers think it does.
They come up with the features and the implementation is an unimportant detail in realizing their designs.
In reality implementation details frequently drive design and in most cases they are at least highly intertwined.
I can’t count how many products and features I’ve built that ended working completely differently than the initial design, or how many times I was able to simplify a workflow after spending a days thinking about the implementation details.
You can kinda do something similar by spending days or weeks going back and forth with an LLM, but at least in my experience that doesn’t really save much time and I don’t understand the problem quite as well by the end of it.