The File System API is a JavaScript API, not an HTML one, so it helps to think about it from that light (programs, not documents). The API allows tools such as photo editors, file converters, code editors, and the like to be given access to a set of files they can work on directly rather than needing to import and export from the browser on every change. If the attack surface is too much for a use case it can be globally denied by default in every major browser so you won't even get prompted.

The page needs permission. That permission step is similar to the act of downloading a native app. Except for the fact that the broswer gives even less access to your system than a native app so it's safer than a native app. (at least on desktop) That file system API is super useful for cloud based IDEs as just one example

Microsoft has an elaborate VS Code demo app that uses this API. Click "Open Folder" to see the API in action): https://vscode.dev