I actually implemented it recently in one of my open-source apps. It's 6 lines of Javascript: Create an <a> element, set the data in its href with:

element.setAttribute("href","data:text/plain;charset=utf-8," +encodeURIComponent(content))

and element.click() followed by document.body.removeChild(element);

This works perfectly fine for saving single files. FileSystem access API is useful when entire directory needs to be stored and perhaps without the standard SaveAs.. UI.