How then are web apps supposed to become part of a more durable workflow (i.e. opening/saving/moving/backing up files) if we do not permit them the same privileges as native apps? I don't think web apps should have total control over your filesystem, but why not at least allow them to operate within a folder?

They aren't. Web apps can't be trusted with access to barely anything on your system, lest they copy it to sell as advertising. As long as the internet is fueled by advertising, essentially all web apps are adware.

Operate within which folder?

BTW both Safari and Firefox are not going to implement the File Access non-standards that Chrome pushes. They expose too much, there are no good ways to limit the exposure etc.