I think most people test at least a happy path of their code end to end. I think we can all agree that your last sentence is far more aspirational than bare minimum standard practice. (“I believe we should be spending our energy thoroughly manually testing a feature to make sure when we brainstormed we actually did get every edge case, and it works well.”)

I did one small side web project by only writing spec tests and prompts and testing the results in a browser, never reading nor editing a single line of generated code. It was something for home and so low stakes, but it worked remarkably well and was much better tested than the typical 2022-era home project of mine.