We've been trialling the Native File System API in our PWA Construct 3 (a browser based game editor -
https://www.construct.net).
I think it's absolutely fantastic, and users love it too - it gives them exactly what they expect from IDE-style software in the browser, such as "Save as" to any location on disk, and the ability to use folder-based projects (that are spread across multiple files).
The security concerns are obviously important but I'm pretty confident it's largely mitigated through the permissions model (which is similar to one Windows Store apps use). Also as noted elsewhere, existing web features already allowed reading files and even entire directories; the writing files part is new, and you cannot choose system directories, or ask for too much (e.g. root of the user directory).
So in short I think this is great news for the web and a big step towards allowing web apps to reach parity with desktop/native apps, while managing to do it in a reasonably safe way.