Enter Storage Scopes! When you enable the feature for a given app, it will think it has the necessary access to files/media, but it only has access to its own, well, storage scope. Furthermore, you can manually add directories/files access with the system picker, much like SAF.
Here's an example: Tachiyomi is a popular manga reader app with offline features that need the invasive WRITE_EXTERNAL_STORAGE permission. It doesn't need that obviously, and should use scoped storage features + SAF. This isn't a problem with Storage Scopes. :)