An example - you are using some web IDE (imagine a self-hosted version of VSCode). You have a few local files open in your browser, editing the code. Now you want to save them - you'd have to "redownload" them to save them. That's a highly suboptimal UX.
If you are actively working on the files, then you could just save them to the app's local storage. There is not necessarily a need to save them back to the same place you imported them from. When you are ready to export the project then you could have the app generate a zip file, or just push it directly to git or another app and skip the filesystem altogether.
Obviously this is not a great workflow for certain things like system administration tools that are specifically designed to work with the local machine's filesystem, but that's not really a good use case for PWAs in the first place.
Local storage is obviously not an option - imagine your project has a few gigabytes. Coding example was just to illustrate the problem quickly for everybody to understand what the issue is.
Forcing user to generate/download ZIP at some well-defined points in time is a horrible UX idea; in addition it leads to desynced content of files and local storage. Browser's local storage can also disappear if SQLite gets corrupted, making it a nice SPOF for all PWAs that are installed. Imagine not losing data just for one app, but for all of them.
