Since this question has gained a lot of attention lately, for anyone interested on the subject there are very exiting news: the Writable Files API (it is now called the File System Access API).
At this time the proposed new APIs are merely in the design phase, and there is a vivid discussion about the opportunity itself of introducing them. So it looks like we are still far from a production ready solution.
UPDATE 2019-04-12
There is now an explainer (also linked in the above mentioned post) with a lot of useful info on how the proposed APIs will/should work.
UPDATE 2021-02-19
The File System Access API is still evolving nicely. On top of the explainer mentioned in the previous update, there is also a draft doc on MDN Web Docs
UPDATE 2021-10-14
A very good starting point to know more about the File System Access API is still this post on web.dev, which is being constantly updated.